diff --git a/proys/InsectPopulation/AutomDiff_V2.jl b/proys/InsectPopulation/AutomDiff_V2.jl new file mode 100644 index 0000000..0b99f5b --- /dev/null +++ b/proys/InsectPopulation/AutomDiff_V2.jl @@ -0,0 +1,95 @@ +#Modulo de Diferenciacion Automatica +#El siguiente modulo define la estructura de los objetos "duales" asi como las operaciones entre ellos. +#Autores: Daniel (https://github.com/danmarurr) y Fernanda (https://github.com/FernandaPerez) + + +__precompile__(true) + +module AD + import Base: +, -, *, /, ^, == + + export Dual, xdual + + + + type Dual{T<:Real} + # código: + fun :: T + der :: T + end + + Dual(a, b) = Dual(promote(a, b) ...) + # Aqui se define un método que garantiza que el dual de un número cumple lo requerido + Dual(a) = Dual(a, zero(0)) + # Aqui se define la función `xdual`, que se usará para identificar la variable independiente + + function xdual(x0) + Dual(x0, one(x0)) + end + + # Definiendo operaciones cuando los argumentos son Duales + +(a::Dual, b::Dual) = Dual(a.fun + b.fun, a.der + b.der) + -(a::Dual, b::Dual) = Dual(a.fun - b.fun, a.der - b.der) + *(a::Dual, b::Dual) = Dual(a.fun * b.fun, a.der*b.fun + b.der*a.fun) + /(a::Dual, b::Dual) = Dual(a.fun / b.fun, (a.der - b.der*(a.fun/b.fun))/b.fun) + ^{T<:Int}(a::Dual, α::T) = Dual(a.fun^α, α*a.fun^(α - 1)*a.der) + ^{T<:Float64}(a::Dual, α::T) = Dual(a.fun^α, α*a.fun^(α - 1)*a.der) + ^{T<:Rational}(a::Dual, α::T) = Dual(a.fun^α, α*a.fun^(α - 1)*a.der) + ^{T<:Irrational}(a::Dual, α::T) = Dual(a.fun^α, α*a.fun^(α - 1)*a.der) + ==(a::Dual, b::Dual) = (a.fun == b.fun && a.der == b.der) + + + # Definiendo operaciones cuando el argumento de la derecha es un número + +{T<:Real}(a::Dual, γ::T) = +(a, Dual(γ)) + -{T<:Real}(a::Dual, γ::T) = -(a, Dual(γ)) + *{T<:Real}(a::Dual, γ::T) = *(a, Dual(γ)) + /{T<:Real}(a::Dual, γ::T) = /(a, Dual(γ)) + + # Definiendo operaciones cuando el argumento de la izquierda es un número + + +{T<:Real}(γ::T, a::Dual) = +(Dual(γ), a) + -{T<:Real}(γ::T, a::Dual) = -(Dual(γ), a) + *{T<:Real}(γ::T, a::Dual) = *(Dual(γ), a) + /{T<:Real}(γ::T, a::Dual) = /(Dual(γ), a) + + +#Importamos todas las funciones para las cuales queremos definir su operacion +import Base: ^, exp, sqrt, cbrt, sin, cos, tan, cot, sec, csc, sinh, cosh, tanh, coth, sech, csch, +asin, acos, atan, acot, asec, acsc, +asinh, acosh, atanh, acoth, asech, acsch + +#Vector con todos los símbolos asociados a las funciones trigométricas, exponenciales, etc. y sus respectivas +#derivadas +Vec_Func = [(:sin, :cos), (:cos, :(x -> -sin(x))), (:tan, :(x -> (sec(x))^2)), (:cot, :(x -> -(csc(x))^2)), + (:sec, :(x -> sec(x)*tan(x))), (:csc, :(x -> -csc(x)*cot(x))), (:sinh, :cosh), (:cosh, :sinh), + (:tanh, :(x -> (sech(x))^2)), (:coth, :(x -> -(csch(x))^2)), (:asin, :(x -> 1/sqrt(1-x^2))), + (:acos, :(x -> -1/sqrt(1-x^2))), (:atan, :(x -> 1/(1+x^2))), (:acot, :(x -> -1/(1+x^2))), + (:asec, :(x -> 1/(sqrt(x^2-1)*x))), (:acsc, :(x -> -1/(sqrt(x^2-1)*x))), (:asinh, :(x -> 1/sqrt(1+x^2))), + (:acosh, :(x -> 1/sqrt(x^2-1))), (:atanh, :(x -> 1/(1-x^2))), (:acoth, :(x -> 1/(1-x^2))), + (:asech, :(x -> 1/(x*sqrt(1-x^2)))), (:acsch, :(x -> -1/(x*sqrt(1+x^2)))), (:sqrt, :(x -> 1/(2*sqrt(x)))), (:exp, :exp), + (:cbrt, :(x -> 1/(3*x^(2/3))))] + +#Casos especiales: los logarítmos y a^x +log(a::Dual) = Dual(log(a.fun), a.der/a.fun) +log{T<:Real}(b::T, a::Dual) = Dual(log(b,a.fun), a.der/(log(b)*a.fun)) +^{T<:Real}(b::T, a::Dual) = Dual(b^a.fun, a.der*log(b)*b^a.fun) + +#Loop para crear los nuevos métodos a partir de los símbolos +for r in 1:length(Vec_Func) + fn = Vec_Func[r][1] #El primer símbolo está asociado a la función + der = Vec_Func[r][2] #El segundo símbolo está asociado a la derivada de la función + ex = quote #Creamos una nueva expresión + function ($fn)(a::Dual) #Definimos fn(a::Dual) + fun = ($fn)(a.fun) + derv = ($der)(a.fun) + return Dual(fun, derv*a.der) #Aplicamos la regla de la cadena + end + end + @eval $ex #Evaluamos la expresión para crear el método +end + + + + +end + 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+50,62,74,86,99,111,123,135,148,160,172,184,197,209,221,233,246,258,270,282,295,307,319,331,344,356,368,380,393,405,417,429,442,454,466,478 +51,63,76,88,101,113,126,138,151,163,176,188,201,213,226,238,251,263,276,288,301,313,326,338,351,363,376,388,401,413,426,438,451,463,476,488 diff --git a/proys/InsectPopulation/PabloProy/finalpopulation.ipynb b/proys/InsectPopulation/PabloProy/finalpopulation.ipynb new file mode 100644 index 0000000..52dbcc8 --- /dev/null +++ b/proys/InsectPopulation/PabloProy/finalpopulation.ipynb @@ -0,0 +1,908 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "# Control de Poblaciones de Insectos al Introducir Insectos Estériles\n", + "\n", + "$$\n", + "N_{t+1}=\\frac{R N_t^2}{(R-1)\\frac{N_t^2}{M}+N_t+S}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "En 1937, E. F. Knipling, propuso la Técnica de Insectos Estériles (SIT, en inglés). La técnica no fue implementada haste 1958 sobre una plaga de `screwworm` en EEUU usando métodos físicos y químicos para causar esterilidad. El método ha sido implementado en México o otros países de Sudamérica con éxito.\n", + "\n", + "\n", + "\n", + "\n", + "Hasta años recientes SIT sigue siendo una técnica usada y estudiada en genética de poblaciones\n", + "\n", + "* `Oliva, C., Damiens, D., Vreysen, M., Lempeiere, G., & Gilles, J. (2013). Reproductive strategies of aedes albopictus (diptera: Culicidae) and implications for the sterile insect technique. Plos One, 8(11), e78884. doi:10.1371/journal.pone.0078884`\n", + "\n", + "\n", + "* `Barnes, B. N., Hofmeyr, J. H., Groenewald, S., Conlong, D. E., & Wohlfarter, M. (2015). The sterile insect technique in agricultural crops in south africa: A metamorphosis …. but will it fly? African Entomology, 23(1), 1-18. doi:10.4001/003.023.0103`\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WARNING: No working GUI backend found for matplotlib.\n" + ] + }, + { + "data": { + "text/plain": [ + "Plots.PyPlotBackend()" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "using Plots, LaTeXStrings\n", + "\n", + "pyplot()" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "f (generic function with 1 method)" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "f(x,α,β,γ) = (α*(x)^2)/((((α-1.0)*(x^2))/β + γ + x))" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "iteramapeo (generic function with 1 method)" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "``` Este código nos permite iterar una función f n veces dada una condición inicial x0. \n", + "``` \n", + "\n", + "function iteramapeo(f, x0, n)\n", + " xx = [x0]\n", + " fx = [0.0]\n", + " for it = 1:n\n", + " x1 = f(x0)\n", + " push!(xx, x0)\n", + " push!(fx, x1)\n", + " x0 = x1\n", + " push!(xx,x1)\n", + " push!(fx,x1)\n", + " end\n", + " xx, fx\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(::#1) (generic function with 1 method)" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "``` Aquí definimos el valor de los parámetros que utilizamos con la convención \\alpha \\equiv R, \\beta \\equiv M,\n", + "``` \\gamma \\equiv S ```\n", + "α=500.0\n", + "β=10.0\n", + "γ=2.0\n", + "func = x -> f(x,α,β,γ)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + " \n", + " \n", + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "using Interact " + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "xfin,ffin = iteramapeo(func,200.0,10);" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false, + "scrolled": false + }, + "outputs": [ + { + "data": { + "text/html": [], + "text/plain": [ + "Interact.Slider{Float64}(Signal{Float64}(100.0, nactions=0),\"γ\",100.0,0.0:1.0:200.0,\".3f\",true)" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "" + ] + }, + "execution_count": 26, + "metadata": { + "comm_id": "dd5ad9fa-6638-4016-ab33-fd67ec618fa2", + "reactive": true + }, + "output_type": "execute_result" + } + ], + "source": [ + "α = 10.0\n", + "β= 20.0\n", + "``` Este codigo genera 200 gráficas para distintos valores de \\gamma y luego hace un .gif almacenado temporalmente\n", + "```\n", + "@manipulate for γ in 0:1.0:200\n", + " pobla(x)=f(x,α,β,γ)\n", + " xfin,ffin = iteramapeo(pobla,10.0,16); #Añade la condición inicial con la que se analiza el mapeo y \n", + " #su trayectoria, la función definida un renglón arriba y el número de iteraciones.\n", + " plot(-10:1/32:100, pobla, xaxis=(L\"x\", (-10.0, 100.0)), yaxis=(L\"F_\\alpha(x)\",(-10.0,20.0)) # Hace la gráfica\n", + " #con especificaciones para ejees.\n", + " title!(\"Analisis grafico para distintos valores de S\")\n", + " plot!(-10:1/32:50, identity) #Grafica la identidad del análisis gráfico\n", + " plot!(xfin, ffin, marker=(:dot, 3, 0.4)) #Señala dónde terminó la condición inicial dada\n", + "end" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Aquí mostrasmos una gráfica del comportamiento temporal del mapeo cuando $S_{c}=0$ y se varía la condición inicial." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false, + "scrolled": true + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/usr/lib/pymodules/python2.7/matplotlib/font_manager.py:1236: UserWarning: findfont: Font family ['Helvetica'] not found. Falling back to Bitstream Vera Sans\n", + " (prop.get_family(), self.defaultFamily[fontext]))\n", + "/usr/lib/pymodules/python2.7/matplotlib/font_manager.py:1246: UserWarning: findfont: Could not match :family=Bitstream Vera Sans:style=normal:variant=normal:weight=normal:stretch=normal:size=8.0. Returning /usr/share/matplotlib/mpl-data/fonts/ttf/cmb10.ttf\n", + " UserWarning)\n", + "/usr/lib/pymodules/python2.7/matplotlib/font_manager.py:1246: UserWarning: findfont: Could not match :family=Bitstream Vera Sans:style=normal:variant=normal:weight=normal:stretch=normal:size=11.0. Returning /usr/share/matplotlib/mpl-data/fonts/ttf/cmb10.ttf\n", + " UserWarning)\n" + ] + }, + { + "data": { + "text/plain": [ + "g (generic function with 1 method)" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "α = 10.0\n", + "β= 25.0\n", + "g(x,α,β)=(α*(x)^2)/((((α-1.0)*(x^2))/β + x)) #Define el mapeo con \\gamma = 0" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/html": [], + "text/plain": [ + "Interact.Slider{Float64}(Signal{Float64}(50.0, nactions=0),\"i\",50.0,0.0:1.0:100.0,\".3f\",true)" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "" + ] + }, + "execution_count": 27, + "metadata": { + "comm_id": "3daa2a7b-cad3-4c69-b2fc-cbf3a2e563a6", + "reactive": true + }, + "output_type": "execute_result" + } + ], + "source": [ + "@manipulate for i in 0:1.0:100 #Este código realiza una gráfica interactiva que cambia la condición inicial\n", + " # en cada paso entre 0 y 100 con los valores de \\alpha y \\beta dados anteriormente.\n", + " poblaciones(i) = g(i,α,β)\n", + " xfin,ffin = iteramapeo(poblaciones,i,20);\n", + " plot(-10:1/32:100, poblaciones, xaxis=(L\"x\", (-10.0,100.0)), yaxis=(L\"F_\\alpha(x)\",(-100.0,100.0)))\n", + " title!(\"Evolucion de la poblacion sin insectos infertiles\")\n", + " plot!(-30:1/32:100, identity)\n", + " plot!(xfin, ffin, marker=(:dot, 3, 0.4))\n", + "end" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Vemos que en éste caso, la población total nunca muere, tal como se esperaba, pues no hay insectos infértiles en este caso." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false + }, + "source": [ + "Se resolvió la ecuación $N(x)-x=0$ para encontrar los puntos fijos del mapeo en términos de los parámetros R,S y M, obteniendo:\n", + "\n", + "$X_{0}= 0$\n", + "\n", + "\n", + "y \n", + "\n", + "\n", + "\n", + "$X_{12}= \\frac{\\pm M(1-R)+\\sqrt{R-1}\\sqrt{M^{2}(1-R)-4MS}}{2(1-R)}$\n", + "\n", + "\n", + "\n", + "Por lo que, para encontrar poblaciones estáticas distintas de cero, tenemos que se deben cumplir las siguientes condiciones:\n", + "\n", + "$R> 1 $ ^ $M > \\frac{4S}{R-1}$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "INFO: Nothing to be done\n", + "INFO: METADATA is out-of-date — you may not have the latest version of Roots\n", + "INFO: Use `Pkg.update()` to get the latest versions of your packages\n" + ] + } + ], + "source": [ + "Pkg.add(\"Roots\")" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "using Roots" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "puntofijo (generic function with 1 method)" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "function puntofijo(F::Function, range) #Este código calcula los puntos fijos de una función F en un rango range.\n", + " pf= fzeros(x -> (F(x) - x) , range)\n", + " return pf\n", + "end " + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "F (generic function with 1 method)" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "α= 10.0\n", + "β= 25.0\n", + "γ= 50.0\n", + "\n", + "F(x) = (α*(x)^2)/((((α-1.0)*(x^2))/β + γ + x)) #Se define la función con nuevos parámetros arbitrarios, pero que\n", + "#cumplen las condiciones mencionadas.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "3-element Array{Float64,1}:\n", + " 0.0 \n", + " 8.33333\n", + " 16.6667 " + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pf=puntofijo(F,[0,20.0]) #Se calculan los puntos fijos de éste mapeo." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "g (generic function with 2 methods)" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "g(x)= (α*(x)^2)/((((α-1.0)*(x^2))/β + γ + x)) -x #Se define el mapeo que nos permite estudiar la localización \n", + "#de los puntos fijos al variar los parámetros." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(::#24) (generic function with 1 method)" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "α= 10.0\n", + "β= 25.0\n", + "γ= 50.0\n", + "func=x -> g(x) #Se dan valores a los parámetros para realizar un ejemplo de sus puntos fijos." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A continuación se muestra una gráfica de los puntos fijos del mapeo en términos de los parámetros\n", + "$R=10$,$M=25$ y $S=50$." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/html": [ + "" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plot(-10:1/32:30, func,xticks=-10:0.5:100,yticks=-10:0.5:50) #Se grafica el mapeo N(X)-x\n", + "xlabel!(L\"x\")\n", + "ylabel!(L\"N(x)-x\")\n", + "title!(\"Puntos fijos de N(x)\")\n", + "plot!([8.3,8.3], [1, -1, 0]) #Se marcan los puntos fijos sobre la gráfica.\n", + "plot!([0,0], [1, -1,0])\n", + "plot!([16.66, 16.66], [1, -1, 0])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A continuación se muestran graficas que relacionan los parámetros y el comportamiento de los puntos fijos dependiendo de éstos." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "La función a estudiar es:\n", + "\n", + "$N(X)-X= \\frac{MRX^{2}}{(R-1)X^{2}+M(X+S)} -X $\n", + "\n", + " Nos interesa encontrar éste mapeo pues nos permite observar el comportamiento de los puntos fijos en función de los parámetros." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "En primer lugar, estudiemos a los puntos fijos para distintas $M$ en cada gráfica en función de $R$ y $S$ para una condición inicial fija $X_{0}=10.0$. " + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "PyPlot.Figure(PyObject )" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "INFO: Saved animation to /home/juser/tmp.gif\n" + ] + }, + { + "data": { + "text/html": [ + "\" />" + ], + "text/plain": [ + "Plots.AnimatedGif(\"/home/juser/tmp.gif\")" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pyplot(leg=false, ticks=nothing) #Este código realiza una gráfica para cada valor de M entre 1 y 80\n", + "x = y = linspace(2.0, 40, 40) #Establece el paso entre cada x,y y sus valores máximo y mínimo.\n", + "zs = zeros(0,40)\n", + "x0= 10.0 #Condición inicial arbitraria\n", + "@gif for i in linspace(1, 80, 100) #Creando el .gif, con 100 imágenes.\n", + " G(x,y) = (x*(x0)^2)/((((x-1.0)*(x0^2))/i + y + x0))-x0\n", + "\n", + "\n", + "plot(x, y, G, st = [:surface, :contourf],xaxis=(L\"R\",(-1.0, 50)),yaxis=(L\"S\",(-1.0, 50)),title=\"Puntos fijos del mapeo para distintas M\")\n", + " \n", + " end" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Ahora estudiamos el comportamiento de los puntos fijos con un valor distinto de $R$ en cada gráfica que varía en función de $M$ y $S$." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "PyPlot.Figure(PyObject )" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "INFO: Saved animation to /home/juser/tmp.gif\n" + ] + }, + { + "data": { + "text/html": [ + "\" />" + ], + "text/plain": [ + "Plots.AnimatedGif(\"/home/juser/tmp.gif\")" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pyplot(leg=false, ticks=nothing) #Este código realiza una gráfica para cada valor de R entre 1 y 100.\n", + "x = y = linspace(2.0, 40, 40)\n", + "zs = zeros(0,40)\n", + "x0= 10.0\n", + "@gif for i in linspace(1,100,100) #Se genera el .gif con 100 imágenes. \n", + " G(x,y) = (i*(x0)^2)/((((i-1.0)*(x0^2))/x + y + x0))-x0\n", + " title!(L\"Puntos fijos del mapeo\")\n", + " p = plot(x, y, G, st = [:surface, :contourf],xaxis=(L\"M\",(-1.0, 50)),yaxis=(L\"S\",(-1.0, 50)),title=\"Puntos fijos del mapeo para distintas R\")\n", + " \n", + " end" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finalmente, observemos la evolución de los puntos fijos para un valor distinto de $S$ en cada gráfica que se encuentra en\n", + "función de $M$ y $R$." + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "PyPlot.Figure(PyObject )" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "INFO: Saved animation to /home/juser/tmp.gif\n" + ] + }, + { + "data": { + "text/html": [ + "\" />" + ], + "text/plain": [ + "Plots.AnimatedGif(\"/home/juser/tmp.gif\")" + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pyplot(leg=false, ticks=nothing) #Este código genera una gŕafica para cada valor de S en función de M y R.\n", + "x = y = linspace(2.0, 80, 90)\n", + "zs = zeros(0,90)\n", + "x0= 50.0 #Se utiliza otra condición inicial.\n", + "@gif for i in linspace(1, 100, 100) #Se construye el .gif con 100 imágenes también.\n", + " G(x,y) = (y*(x0)^2)/((((y-1.0)*(x0^2))/x + i + x0))-x0\n", + " title!(L\"Puntos fijos del mapeo\")\n", + " p = plot(x, y, G, st = [:surface, :contourf],xaxis=(L\"M\",(-1.0,100)),yaxis=(L\"R\",(-1.0, 100)),title=\"Puntos fijos del mapeo para distintas S\")\n", + " \n", + "end" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "celltoolbar": "Slideshow", + "kernelspec": { + "display_name": "Julia 0.5.0", + "language": "julia", + "name": "julia-0.5" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "0.5.0" + }, + "widgets": { + "state": { + "1a72896c-621a-4f4a-ad21-0358c2e061ba": { + "views": [ + { + "cell_index": 13 + } + ] + }, + "c6205deb-bbae-450c-bb19-6cb88744793d": { + "views": [ + { + "cell_index": 10 + } + ] + } + }, + "version": "1.2.0" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/proys/InsectPopulation/PabloProy/population.ipynb b/proys/InsectPopulation/PabloProy/population.ipynb new file mode 100644 index 0000000..2b14d70 --- /dev/null +++ b/proys/InsectPopulation/PabloProy/population.ipynb @@ -0,0 +1,1127 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "INFO: Nothing to be done\n", + "INFO: METADATA is out-of-date — you may not have the latest version of Plots\n", + "INFO: Use `Pkg.update()` to get the latest versions of your packages\n" + ] + } + ], + "source": [ + "Pkg.add(\"Plots\")" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "INFO: Updating cache of StatPlots...\n", + "INFO: Installing AxisAlgorithms v0.1.5\n", + "INFO: Installing Interpolations v0.3.6\n", + "INFO: Installing KernelDensity v0.3.0\n", + "INFO: Installing PlotRecipes v0.1.0\n", + "INFO: Installing Ratios v0.0.4\n", + "INFO: Installing StatPlots v0.1.1\n", + "INFO: Installing WoodburyMatrices v0.2.0\n", + "INFO: Building Rmath\n", + "INFO: Building Plots\n", + "INFO: Cannot find deps/plotly-latest.min.js... downloading latest version.\n", + " % Total % Received % Xferd Average Speed Time Time Time Current\n", + " Dload Upload Total Spent Left Speed\n", + " 0 0 0 0 0 0 0 0 --:--:-- --:--:-- --:--:-- 0curl: (77) error setting certificate verify locations:\n", + " CAfile: /etc/pki/tls/certs/ca-bundle.crt\n", + " CApath: none\n", + "================================[ ERROR: Plots ]================================\n", + "\n", + "LoadError: failed process: Process(`curl -o /home/sof9409/.julia/v0.5/Plots/deps/plotly-latest.min.js -L https://cdn.plot.ly/plotly-latest.min.js`, ProcessExited(77)) [77]\n", + "while loading /home/sof9409/.julia/v0.5/Plots/deps/build.jl, in expression starting on line 7\n", + "\n", + "================================================================================\n", + "\n", + "================================[ BUILD ERRORS ]================================\n", + "\n", + "WARNING: Plots had build errors.\n", + "\n", + " - packages with build errors remain installed in /home/sof9409/.julia/v0.5\n", + " - build the package(s) and all dependencies with `Pkg.build(\"Plots\")`\n", + " - build a single package by running its `deps/build.jl` script\n", + "\n", + "================================================================================\n", + "INFO: Package database updated\n", + "INFO: METADATA is out-of-date — you may not have the latest version of PlotRecipes\n", + "INFO: Use `Pkg.update()` to get the latest versions of your packages\n" + ] + } + ], + "source": [ + "Pkg.add(\"PlotRecipes\")" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "INFO: Nothing to be done\n", + "INFO: METADATA is out-of-date — you may not have the latest version of PyPlot\n", + "INFO: Use `Pkg.update()` to get the latest versions of your packages\n" + ] + } + ], + "source": [ + "Pkg.add(\"PyPlot\")" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false, + "scrolled": true + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "INFO: Updating METADATA...\n", + "INFO: Updating cache of Polynomials...\n", + "INFO: Updating cache of PlotRecipes...\n", + "INFO: Updating cache of PlotUtils...\n", + "INFO: Updating cache of Plots...\n", + "INFO: Updating cache of FixedSizeArrays...\n", + "INFO: Updating cache of NaNMath...\n", + "INFO: Updating cache of ForwardDiff...\n", + "INFO: Updating cache of Compat...\n", + "INFO: Updating cache of SHA...\n", + "INFO: Updating cache of PDMats...\n", + "INFO: Updating cache of PositiveFactorizations...\n", + "INFO: Updating Plotly master...\n", + "INFO: Computing changes...\n", + "INFO: Cloning cache of GeometryTypes from https://github.com/JuliaGeometry/GeometryTypes.jl.git\n", + "INFO: Cloning cache of NetworkLayout from https://github.com/JuliaGraphs/NetworkLayout.jl.git\n", + "INFO: Cloning cache of PlotThemes from https://github.com/JuliaPlots/PlotThemes.jl.git\n", + "INFO: Upgrading Blink: v0.4.3 => v0.4.4\n", + "INFO: Upgrading Compat: v0.9.3 => v0.9.5\n", + "INFO: Upgrading Conda: v0.3.2 => v0.4.0\n", + "INFO: Upgrading DataArrays: v0.3.9 => v0.3.10\n", + "INFO: Upgrading DataFrames: v0.8.4 => v0.8.5\n", + "INFO: Upgrading DocStringExtensions: v0.2.1 => v0.3.0\n", + "INFO: Upgrading FixedSizeArrays: v0.2.4 => v0.2.5\n", + "INFO: Installing GeometryTypes v0.2.1\n", + "INFO: Upgrading Juno: v0.2.3 => v0.2.5\n", + "INFO: Upgrading Media: v0.2.3 => v0.2.4\n", + "INFO: Upgrading NaNMath: v0.2.1 => v0.2.2\n", + "INFO: Installing NetworkLayout v0.0.1\n", + "INFO: Upgrading PDMats: v0.5.0 => v0.5.1\n", + "INFO: Upgrading PlotRecipes: v0.1.0 => v0.2.0\n", + "INFO: Installing PlotThemes v0.1.0\n", + "INFO: Upgrading PlotUtils: v0.1.1 => v0.2.0\n", + "INFO: Upgrading Plots: v0.9.4 => v0.10.1\n", + "INFO: Upgrading Polynomials: v0.1.0 => v0.1.1\n", + "INFO: Upgrading PositiveFactorizations: v0.0.2 => v0.0.3\n", + "INFO: Upgrading SHA: v0.2.1 => v0.3.0\n", + "INFO: Upgrading StatPlots: v0.1.1 => v0.2.0\n", + "INFO: Building HttpParser\n", + "INFO: Attempting to Create directory /home/sof9409/.julia/v0.5/HttpParser/deps/downloads\n", + "INFO: Directory /home/sof9409/.julia/v0.5/HttpParser/deps/downloads already created\n", + "INFO: Attempting to Create directory /home/sof9409/.julia/v0.5/HttpParser/deps/downloads\n", + "INFO: Directory /home/sof9409/.julia/v0.5/HttpParser/deps/downloads already created\n", + "INFO: Downloading file https://github.com/nodejs/http-parser/archive/v2.7.1.zip\n", + " % Total % Received % Xferd Average Speed Time Time Time Current\n", + " Dload Upload Total Spent Left Speed\n", + " 0 0 0 0 0 0 0 0 --:--:-- --:--:-- --:--:-- 0curl: (77) error setting certificate verify locations:\n", + " CAfile: /etc/pki/tls/certs/ca-bundle.crt\n", + " CApath: none\n", + "=============================[ ERROR: HttpParser ]==============================\n", + "\n", + "LoadError: failed process: Process(`curl -f -o /home/sof9409/.julia/v0.5/HttpParser/deps/downloads/v2.7.1.zip -L https://github.com/nodejs/http-parser/archive/v2.7.1.zip`, ProcessExited(77)) [77]\n", + "while loading /home/sof9409/.julia/v0.5/HttpParser/deps/build.jl, in expression starting on line 71\n", + "\n", + "================================================================================\n", + "INFO: Building MbedTLS\n", + "INFO: Attempting to Create directory /home/sof9409/.julia/v0.5/MbedTLS/deps/downloads\n", + "INFO: Directory /home/sof9409/.julia/v0.5/MbedTLS/deps/downloads already created\n", + "INFO: Downloading file https://cache.julialang.org/https://tls.mbed.org/download/mbedtls-2.1.1-apache.tgz\n", + " % Total % Received % Xferd Average Speed Time Time Time Current\n", + " Dload Upload Total Spent Left Speed\n", + " 0 0 0 0 0 0 0 0 --:--:-- --:--:-- --:--:-- 0curl: (77) error setting certificate verify locations:\n", + " CAfile: /etc/pki/tls/certs/ca-bundle.crt\n", + " CApath: none\n", + "===============================[ ERROR: MbedTLS ]===============================\n", + "\n", + "LoadError: failed process: Process(`curl -f -o /home/sof9409/.julia/v0.5/MbedTLS/deps/downloads/mbedtls-2.1.1-apache.tgz -L https://cache.julialang.org/https://tls.mbed.org/download/mbedtls-2.1.1-apache.tgz`, ProcessExited(77)) [77]\n", + "while loading /home/sof9409/.julia/v0.5/MbedTLS/deps/build.jl, in expression starting on line 74\n", + "\n", + "================================================================================\n", + "INFO: Building Conda\n", + "INFO: Building Plots\n", + "INFO: Cannot find deps/plotly-latest.min.js... downloading latest version.\n", + " % Total % Received % Xferd Average Speed Time Time Time Current\n", + " Dload Upload Total Spent Left Speed\n", + " 0 0 0 0 0 0 0 0 --:--:-- --:--:-- --:--:-- 0curl: (77) error setting certificate verify locations:\n", + " CAfile: /etc/pki/tls/certs/ca-bundle.crt\n", + " CApath: none\n", + "================================[ ERROR: Plots ]================================\n", + "\n", + "LoadError: failed process: Process(`curl -o /home/sof9409/.julia/v0.5/Plots/deps/plotly-latest.min.js -L https://cdn.plot.ly/plotly-latest.min.js`, ProcessExited(77)) [77]\n", + "while loading /home/sof9409/.julia/v0.5/Plots/deps/build.jl, in expression starting on line 7\n", + "\n", + "================================================================================\n", + "INFO: Building Rmath\n", + "\n", + "================================[ BUILD ERRORS ]================================\n", + "\n", + "WARNING: HttpParser, Plots and MbedTLS had build errors.\n", + "\n", + " - packages with build errors remain installed in /home/sof9409/.julia/v0.5\n", + " - build the package(s) and all dependencies with `Pkg.build(\"HttpParser\", \"Plots\", \"MbedTLS\")`\n", + " - build a single package by running its `deps/build.jl` script\n", + "\n", + "================================================================================\n" + ] + } + ], + "source": [ + "Pkg.update()" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "INFO: Recompiling stale cache file /home/sof9409/.julia/lib/v0.5/Plots.ji for module Plots.\n", + "WARNING: Module Compat with uuid 9309146622058 is missing from the cache.\n", + "This may mean module Compat does not support precompilation but is imported by a module that does.\n", + "ERROR: LoadError: Declaring __precompile__(false) is not allowed in files that are being precompiled.\n", + " in require(::Symbol) at ./loading.jl:385\n", + " in include_from_node1(::String) at ./loading.jl:488\n", + " in macro expansion; at ./none:2 [inlined]\n", + " in anonymous at ./:?\n", + " in eval(::Module, ::Any) at ./boot.jl:234\n", + " in process_options(::Base.JLOptions) at ./client.jl:239\n", + " in _start() at ./client.jl:318\n", + "while loading /home/sof9409/.julia/v0.5/FixedSizeArrays/src/FixedSizeArrays.jl, in expression starting on line 4\n", + "ERROR: LoadError: Failed to precompile FixedSizeArrays to /home/sof9409/.julia/lib/v0.5/FixedSizeArrays.ji.\n", + " in compilecache(::String) at ./loading.jl:593\n", + " in require(::Symbol) at ./loading.jl:393\n", + " in include_from_node1(::String) at ./loading.jl:488\n", + " in macro expansion; at ./none:2 [inlined]\n", + " in anonymous at ./:?\n", + " in eval(::Module, ::Any) at ./boot.jl:234\n", + " in process_options(::Base.JLOptions) at ./client.jl:239\n", + " in _start() at ./client.jl:318\n", + "while loading /home/sof9409/.julia/v0.5/Plots/src/Plots.jl, in expression starting on line 5\n" + ] + }, + { + "ename": "LoadError", + "evalue": "LoadError: Failed to precompile Plots to /home/sof9409/.julia/lib/v0.5/Plots.ji.\nwhile loading In[5], in expression starting on line 1", + "output_type": "error", + "traceback": [ + "LoadError: Failed to precompile Plots to /home/sof9409/.julia/lib/v0.5/Plots.ji.\nwhile loading In[5], in expression starting on line 1", + "", + " in compilecache(::String) at ./loading.jl:593", + " in require(::Symbol) at ./loading.jl:393" + ] + } + ], + "source": [ + "using Plots, LaTeXStrings\n", + "\n", + "pyplot()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "f (generic function with 1 method)" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "f(x,α,β,γ) = (α*(x)^2)/((((α-1.0)*(x^2))/β + γ + x))" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "iteramapeo (generic function with 1 method)" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "function iteramapeo(f, x0, n)\n", + " xx = [x0]\n", + " fx = [0.0]\n", + " for it = 1:n\n", + " x1 = f(x0)\n", + " push!(xx, x0)\n", + " push!(fx, x1)\n", + " x0 = x1\n", + " push!(xx,x1)\n", + " push!(fx,x1)\n", + " end\n", + " xx, fx\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(::#1) (generic function with 1 method)" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "α=500.0\n", + "β=10.0\n", + "γ=2.0\n", + "func = x -> f(x,α,β,γ)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "xfin,ffin = iteramapeo(func,10.0,14);" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "ename": "LoadError", + "evalue": "LoadError: UndefVarError: @L_str not defined\nwhile loading In[10], in expression starting on line 1", + "output_type": "error", + "traceback": [ + "LoadError: UndefVarError: @L_str not defined\nwhile loading In[10], in expression starting on line 1", + "" + ] + } + ], + "source": [ + "plot(-10:1/32:10, func, xaxis=(L\"x\", (-1.0, 6.0)), yaxis=(L\"F_\\alpha(x)\",(-1.0,3.0)))\n", + "plot!(-10:1/32:10, identity)\n", + "plot!(xfin, ffin, marker=(:dot, 3, 0.4))" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(::#3) (generic function with 1 method)" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "α=500.0\n", + "β=10.0\n", + "γ=2.0\n", + "func = x -> f(x,α,β,γ)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "xfin,ffin = iteramapeo(func,200.0,10);" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "scrolled": false + }, + "outputs": [ + { + "ename": "LoadError", + "evalue": "LoadError: UndefVarError: @L_str not defined\nwhile loading In[13], in expression starting on line 1", + "output_type": "error", + "traceback": [ + "LoadError: UndefVarError: @L_str not defined\nwhile loading In[13], in expression starting on line 1", + "" + ] + } + ], + "source": [ + "plot(-10:1/32:10, func, xaxis=(L\"x\", (-1.0, 6.0)), yaxis=(L\"F_\\alpha(x)\",(-1.0,3.0)))\n", + "plot!(-10:1/32:10, identity)\n", + "plot!(xfin, ffin, marker=(:dot, 3, 0.4))" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false, + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + " \n", + " \n", + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "using Interact " + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "xfin,ffin = iteramapeo(func,200.0,10);" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false, + "scrolled": true + }, + "outputs": [ + { + "ename": "LoadError", + "evalue": "LoadError: UndefVarError: @L_str not defined\nwhile loading In[16], in expression starting on line 3", + "output_type": "error", + "traceback": [ + "LoadError: UndefVarError: @L_str not defined\nwhile loading In[16], in expression starting on line 3", + "" + ] + } + ], + "source": [ + "α = 10.0\n", + "β= 20.0\n", + "@manipulate for γ in 0:1.0:200\n", + " pobla(x)=f(x,α,β,γ)\n", + " xfin,ffin = iteramapeo(pobla,10.0,16);\n", + " plot(-10:1/32:100, pobla, xaxis=(L\"x\", (-10.0, 100.0)), yaxis=(L\"F_\\alpha(x)\",(-10.0,10.0)))\n", + "plot!(-10:1/32:50, identity)\n", + "plot!(xfin, ffin, marker=(:dot, 3, 0.4))\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "g (generic function with 1 method)" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "α = 10.0\n", + "β= 20.0\n", + "g(x)=(α*(x)^2)/((((α-1.0)*(x^2))/β + x))" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "ename": "LoadError", + "evalue": "LoadError: UndefVarError: @L_str not defined\nwhile loading In[18], in expression starting on line 2", + "output_type": "error", + "traceback": [ + "LoadError: UndefVarError: @L_str not defined\nwhile loading In[18], in expression starting on line 2", + "" + ] + } + ], + "source": [ + "\n", + "@manipulate for i in 1:1.0:100\n", + " funcion(i)=g(i)\n", + " plot(-10:1/32:100, funcion, xaxis=(L\"x\", (-100.0, 100.0)), yaxis=(L\"F_\\alpha(x)\",(-100.0,100.0)))\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false + }, + "source": [ + "Se resolvió la ecuación $N(x)-x=0$ para encontrar los puntos fijos del mapeo en términos de los parámetros R,S y M, obteniendo:\n", + "\n", + "$X_{0}= 0$\n", + "\n", + "\n", + "y \n", + "\n", + "\n", + "\n", + "$X_{12}= \\frac{\\pm M(1-R)+\\sqrt{R-1}\\sqrt{M^{2}(1-R)-4MS}}{2(1-R)}$\n", + "\n", + "\n", + "\n", + "Por lo que, para encontrar poblaciones estáticas distintas de cero, tenemos que se deben cumplir las siguientes condiciones:\n", + "\n", + "$R> 1 $ ^ $M > \\frac{4S}{R-1}$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "INFO: Nothing to be done\n" + ] + } + ], + "source": [ + "Pkg.add(\"Roots\")" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "INFO: Recompiling stale cache file /home/sof9409/.julia/lib/v0.5/Polynomials.ji for module Polynomials.\n", + "WARNING: Module Compat with uuid 9309146622058 is missing from the cache.\n", + "This may mean module Compat does not support precompilation but is imported by a module that does.\n", + "ERROR: LoadError: Declaring __precompile__(false) is not allowed in files that are being precompiled.\n", + " in require(::Symbol) at ./loading.jl:385\n", + " in include_from_node1(::String) at ./loading.jl:488\n", + " in macro expansion; at ./none:2 [inlined]\n", + " in anonymous at ./:?\n", + " in eval(::Module, ::Any) at ./boot.jl:234\n", + " in process_options(::Base.JLOptions) at ./client.jl:239\n", + " in _start() at ./client.jl:318\n", + "while loading /home/sof9409/.julia/v0.5/Polynomials/src/Polynomials.jl, in expression starting on line 8\n" + ] + }, + { + "ename": "LoadError", + "evalue": "LoadError: Failed to precompile Polynomials to /home/sof9409/.julia/lib/v0.5/Polynomials.ji.\nwhile loading In[20], in expression starting on line 1", + "output_type": "error", + "traceback": [ + "LoadError: Failed to precompile Polynomials to /home/sof9409/.julia/lib/v0.5/Polynomials.ji.\nwhile loading In[20], in expression starting on line 1", + "", + " in compilecache(::String) at ./loading.jl:593", + " in require(::Symbol) at ./loading.jl:393", + " in _include_from_serialized(::String) at ./loading.jl:150", + " in _require_from_serialized(::Int64, ::Symbol, ::String, ::Bool) at ./loading.jl:187", + " in _require_search_from_serialized(::Int64, ::Symbol, ::String, ::Bool) at ./loading.jl:217", + " in require(::Symbol) at ./loading.jl:371" + ] + } + ], + "source": [ + "using Roots" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "puntofijo (generic function with 1 method)" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "function puntofijo(F::Function, range)\n", + " pf= fzeros(x -> (F(x) - x) , range)\n", + " return pf\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "F (generic function with 1 method)" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "α= 10.0\n", + "β= 25.0\n", + "γ= 50.0\n", + "\n", + "F(x) = (α*(x)^2)/((((α-1.0)*(x^2))/β + γ + x))\n" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "ename": "LoadError", + "evalue": "LoadError: UndefVarError: fzeros not defined\nwhile loading In[23], in expression starting on line 1", + "output_type": "error", + "traceback": [ + "LoadError: UndefVarError: fzeros not defined\nwhile loading In[23], in expression starting on line 1", + "", + " in puntofijo(::#F, ::Array{Float64,1}) at ./In[21]:2" + ] + } + ], + "source": [ + "pf=puntofijo(F,[0,20.0])" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WARNING: Method definition g(Any) in module Main at In[17]:3 overwritten at In[24]:1.\n" + ] + }, + { + "data": { + "text/plain": [ + "g (generic function with 1 method)" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "g(x)= (α*(x)^2)/((((α-1.0)*(x^2))/β + γ + x)) -x " + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false, + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(::#20) (generic function with 1 method)" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "α= 10.0\n", + "β= 25.0\n", + "γ= 50.0\n", + "func=x -> g(x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A continuación se muestra una gráfica de los puntos fijos del mapeo en términos de los parámetros\n", + "$R=10$,$M=25$ y $S=50$." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "ename": "LoadError", + "evalue": "LoadError: UndefVarError: plot not defined\nwhile loading In[26], in expression starting on line 1", + "output_type": "error", + "traceback": [ + "LoadError: UndefVarError: plot not defined\nwhile loading In[26], in expression starting on line 1", + "" + ] + } + ], + "source": [ + "plot(-10:1/32:30, func,xticks=-10:0.5:100,yticks=-10:0.5:50)\n", + "xlabel!(L\"x\")\n", + "ylabel!(L\"N(x)-x\")\n", + "title!(\"Puntos fijos de N(x)\")\n", + "plot!([8.3,8.3], [1, -1, 0])\n", + "plot!([0,0], [1, -1,0])\n", + "plot!([16.66, 16.66], [1, -1, 0])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A continuación se muestran graficas que relacionan los parámetros y el comportamiento de los puntos fijos dependiendo de éstos." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "La función a estudiar es:\n", + "\n", + "$N(X)-X= \\frac{MRX^{2}}{(R-1)X^{2}+M(X+S)} -X $\n", + "\n", + " Nos interesa encontrar éste mapeo pues nos permite observar el comportamiento de los puntos fijos en función de los parámetros." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "En primer lugar, estudiemos a los puntos fijos para distintas $M$ en cada gráfica en función de $R$ y $S$ para una condición inicial fija $X_{0}=10.0$. " + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "ename": "LoadError", + "evalue": "LoadError: UndefVarError: pyplot not defined\nwhile loading In[27], in expression starting on line 1", + "output_type": "error", + "traceback": [ + "LoadError: UndefVarError: pyplot not defined\nwhile loading In[27], in expression starting on line 1", + "" + ] + } + ], + "source": [ + "pyplot(leg=false, ticks=nothing)\n", + "x = y = linspace(2.0, 40, 40)\n", + "zs = zeros(0,40)\n", + "x0= 10.0\n", + "@gif for i in linspace(1, 80, 5)\n", + " G(x,y) = (x*(x0)^2)/((((x-1.0)*(x0^2))/i + y + x0))-x0\n", + "\n", + " # create a plot with 3 subplots and a custom layout\n", + " # l = @layout [a{0.9w}]\n", + "\n", + " plot(x, y, G, st = [:surface, :contourf],xaxis=(L\"R\",(-1.0, 50)),yaxis=(L\"S\",(-1.0, 50)),title=\"Puntos fijos del mapeo para distintas M\")\n", + " \n", + " end" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Ahora estudiamos el comportamiento de los puntos fijos con un valor distinto de $R$ en cada gráfica que varía en función de $M$ y $S$." + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "ename": "LoadError", + "evalue": "LoadError: UndefVarError: pyplot not defined\nwhile loading In[28], in expression starting on line 1", + "output_type": "error", + "traceback": [ + "LoadError: UndefVarError: pyplot not defined\nwhile loading In[28], in expression starting on line 1", + "" + ] + } + ], + "source": [ + "pyplot(leg=false, ticks=nothing)\n", + "x = y = linspace(2.0, 40, 40)\n", + "zs = zeros(0,40)\n", + "x0= 10.0\n", + "@gif for i in linspace(1,100,5)\n", + " G(x,y) = (i*(x0)^2)/((((i-1.0)*(x0^2))/x + y + x0))-x0\n", + "\n", + " # create a plot with 3 subplots and a custom layout\n", + " title!(L\"Puntos fijos del mapeo\")\n", + " p = plot(x, y, G, st = [:surface, :contourf],xaxis=(L\"M\",(-1.0, 50)),yaxis=(L\"S\",(-1.0, 50)),title=\"Puntos fijos del mapeo para distintas R\")\n", + " \n", + " end" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finalmente, observemos la evolución de los puntos fijos para un valor distinto de $S$ en cada gráfica que se encuentra en\n", + "función de $M$ y $R$." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "ename": "LoadError", + "evalue": "LoadError: UndefVarError: pyplot not defined\nwhile loading In[29], in expression starting on line 1", + "output_type": "error", + "traceback": [ + "LoadError: UndefVarError: pyplot not defined\nwhile loading In[29], in expression starting on line 1", + "" + ] + } + ], + "source": [ + "pyplot(leg=false, ticks=nothing)\n", + "x = y = linspace(2.0, 60, 60)\n", + "zs = zeros(0,60)\n", + "x0= 10.0\n", + "@gif for i in linspace(1, 80, 5)\n", + " G(x,y) = (y*(x0)^2)/((((y-1.0)*(x0^2))/x + i + x0))-x0\n", + "\n", + " # create a plot with 3 subplots and a custom layout\n", + " title!(L\"Puntos fijos del mapeo\")\n", + " p = plot(x, y, G, st = [:surface, :contourf],xaxis=(L\"M\",(-1.0, 50)),yaxis=(L\"R\",(-1.0, 50)),title=\"Puntos fijos del mapeo para distintas S\")\n", + " \n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernelspec": { + "display_name": "Julia 0.5.0", + "language": "julia", + "name": "julia-0.5" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "0.5.0" + }, + "widgets": { + "state": { + "5106949f-6478-4b30-8cc4-b23f3bf1b7bd": { + "views": [ + { + "cell_index": 15 + } + ] + }, + "905096df-477a-4938-b280-991bbb9ae467": { + "views": [ + { + "cell_index": 17 + } + ] + }, + "9ee57ccf-20b1-41c6-8a38-36d91604bc0f": { + "views": [ + { + "cell_index": 15 + } + ] + } + }, + "version": "1.2.0" + } + }, + "nbformat": 4, + "nbformat_minor": 1 +} diff --git a/proys/InsectPopulation/ProyDaniel/AutomDiff_V2.jl b/proys/InsectPopulation/ProyDaniel/AutomDiff_V2.jl new file mode 100755 index 0000000..ce810a1 --- /dev/null +++ b/proys/InsectPopulation/ProyDaniel/AutomDiff_V2.jl @@ -0,0 +1,95 @@ +#Modulo de Diferenciacion Automatica +#El siguiente modulo define la estructura de los objetos "duales" asi como las operaciones entre ellos. +#Autores: Daniel (https://github.com/danmarurr) y Fernanda (https://github.com/FernandaPerez) + + +__precompile__(true) + +module AD + import Base: +, -, *, /, ^, == + + export Dual, xdual + + + + type Dual{T<:Real} + # código: + fun :: T + der :: T + end + + Dual(a, b) = Dual(promote(a, b) ...) + # Aqui se define un método que garantiza que el dual de un número cumple lo requerido + Dual(a) = Dual(a, zero(0)) + # Aqui se define la función `xdual`, que se usará para identificar la variable independiente + + function xdual(x0) + Dual(x0, one(x0)) + end + + # Definiendo operaciones cuando los argumentos son Duales + +(a::Dual, b::Dual) = Dual(a.fun + b.fun, a.der + b.der) + -(a::Dual, b::Dual) = Dual(a.fun - b.fun, a.der - b.der) + *(a::Dual, b::Dual) = Dual(a.fun * b.fun, a.der*b.fun + b.der*a.fun) + /(a::Dual, b::Dual) = Dual(a.fun / b.fun, (a.der - b.der*(a.fun/b.fun))/b.fun) + ^{T<:Int}(a::Dual, α::T) = Dual(a.fun^α, α*a.fun^(α - 1)*a.der) + ^{T<:Float64}(a::Dual, α::T) = Dual(a.fun^α, α*a.fun^(α - 1)*a.der) + ^{T<:Rational}(a::Dual, α::T) = Dual(a.fun^α, α*a.fun^(α - 1)*a.der) + ^{T<:Irrational}(a::Dual, α::T) = Dual(a.fun^α, α*a.fun^(α - 1)*a.der) + ==(a::Dual, b::Dual) = (a.fun == b.fun && a.der == b.der) + + + # Definiendo operaciones cuando el argumento de la derecha es un número + *{T<:Real}(β :: T, a :: Dual) = Dual(a.fun*β, a.der*β ) + +{T<:Real}(a::Dual, γ::T)= +(a::Dual, Dual(γ)) + -{T<:Real}(a::Dual, γ::T)= -(a::Dual, Dual(γ)) + *{T<:Real}(a::Dual, γ::T)= *(a::Dual, Dual(γ)) + /{T<:Real}(a::Dual, γ::T)= /(a::Dual, Dual(γ)) + + # Definiendo operaciones cuando el argumento de la izquierda es un número + + +{T<:Real}(γ::T, a::Dual)= +(Dual(γ), a) + -{T<:Real}(γ::T, a::Dual)= -(Dual(γ), a) + /{T<:Real}(γ::T, a::Dual)= /(Dual(γ), a) + + +#Importamos todas las funciones para las cuales queremos definir su operacion +import Base: ^, exp, sqrt, cbrt, sin, cos, tan, cot, sec, csc, sinh, cosh, tanh, coth, sech, csch, +asin, acos, atan, acot, asec, acsc, +asinh, acosh, atanh, acoth, asech, acsch + +#Vector con todos los símbolos asociados a las funciones trigométricas, exponenciales, etc. y sus respectivas +#derivadas +Vec_Func = [(:sin, :cos), (:cos, :(x -> -sin(x))), (:tan, :(x -> (sec(x))^2)), (:cot, :(x -> -(csc(x))^2)), + (:sec, :(x -> sec(x)*tan(x))), (:csc, :(x -> -csc(x)*cot(x))), (:sinh, :cosh), (:cosh, :sinh), + (:tanh, :(x -> (sech(x))^2)), (:coth, :(x -> -(csch(x))^2)), (:asin, :(x -> 1/sqrt(1-x^2))), + (:acos, :(x -> -1/sqrt(1-x^2))), (:atan, :(x -> 1/(1+x^2))), (:acot, :(x -> -1/(1+x^2))), + (:asec, :(x -> 1/(sqrt(x^2-1)*x))), (:acsc, :(x -> -1/(sqrt(x^2-1)*x))), (:asinh, :(x -> 1/sqrt(1+x^2))), + (:acosh, :(x -> 1/sqrt(x^2-1))), (:atanh, :(x -> 1/(1-x^2))), (:acoth, :(x -> 1/(1-x^2))), + (:asech, :(x -> 1/(x*sqrt(1-x^2)))), (:acsch, :(x -> -1/(x*sqrt(1+x^2)))), (:sqrt, :(x -> 1/(2*sqrt(x)))), (:exp, :exp), + (:cbrt, :(x -> 1/(3*x^(2/3))))] + +#Casos especiales: los logarítmos y a^x +log(a::Dual) = Dual(log(a.fun), a.der/a.fun) +log{T<:Real}(b::T, a::Dual) = Dual(log(b,a.fun), a.der/(log(b)*a.fun)) +^{T<:Real}(b::T, a::Dual) = Dual(b^a.fun, a.der*log(b)*b^a.fun) + +#Loop para crear los nuevos métodos a partir de los símbolos +for r in 1:length(Vec_Func) + fn = Vec_Func[r][1] #El primer símbolo está asociado a la función + der = Vec_Func[r][2] #El segundo símbolo está asociado a la derivada de la función + ex = quote #Creamos una nueva expresión + function ($fn)(a::Dual) #Definimos fn(a::Dual) + fun = ($fn)(a.fun) + derv = ($der)(a.fun) + return Dual(fun, derv*a.der) #Aplicamos la regla de la cadena + end + end + @eval $ex #Evaluamos la expresión para crear el método +end + + + + +end + diff --git a/proys/InsectPopulation/ProyDaniel/Finding Sc.ipynb b/proys/InsectPopulation/ProyDaniel/Finding Sc.ipynb new file mode 100644 index 0000000..a57e1fe --- /dev/null +++ b/proys/InsectPopulation/ProyDaniel/Finding Sc.ipynb @@ -0,0 +1,699 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T13:05:16.448219", + "start_time": "2016-12-05T19:05:16.375Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WARNING: replacing module AD\n", + "WARNING: ignoring conflicting import of AD.Dual into Main\n", + "WARNING: ignoring conflicting import of AD.xdual into Main\n" + ] + }, + { + "data": { + "text/plain": [ + "Plots.PyPlotBackend()" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "#Paquetería necesaria\n", + "using Plots, Interact, LaTeXStrings\n", + "include(\"AutomDiff_V2.jl\")\n", + "import AD: Dual, xdual\n", + "pyplot(legend = :false, size = (500, 500))" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T13:01:36.536930", + "start_time": "2016-12-05T19:01:36.383Z" + }, + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "mapins (generic function with 1 method)" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "#El mapeo que estudiaremos\n", + "mapins(x, M, S, R) = (R*x^2)/((R - 1)*(x^2)/M + S + x)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T13:02:01.631819", + "start_time": "2016-12-05T19:02:01.402Z" + }, + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "mapeo_liap_all" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "#Código para bifurcaciones y Lyapunov que usamos a lo largo del curso\n", + "\"\"\"\n", + " ciclosestables!(xx, f, nit, nout, cc)\n", + "\n", + "Esta función itera el mapeo `f`, de una variable, `nit+nout` veces, \n", + "usando como condición inicial `x0=0`; los últimos `nout` iterados \n", + "actualizan al vector `xx` que tiene longitud `nout`. `cc` es el valor\n", + "del parámetro del mapeo `f`. El mapeo `f` debe ser definido de \n", + "tal manera que `f(x0,cc)` tenga sentido. La idea es los últimos \n", + "`nout` iterados reflejen los ciclos estables del mapeo `f`. \n", + "\"\"\"\n", + "function ciclosestables!(xx, f, nit, nout, cc)\n", + " @assert nit > 0 && nout > 0\n", + " \n", + " # Primeros nit iterados\n", + " x0 = 1000.0\n", + " for it = 1:nit\n", + " x0 = f(x0, cc)\n", + " end\n", + " \n", + " # Se guardan los siguientes nout iterados\n", + " for it = 1:nout\n", + " x0 = f(x0, cc)\n", + " @inbounds xx[it] = x0\n", + " end\n", + " \n", + " nothing\n", + "end\n", + "\"\"\"\n", + " diagbifurc(f, nit, nout, crange)\n", + "\n", + "Itera el mapeo `f` `nit+nout` veces y regresa una matriz\n", + "cuya columna `i` tiene los últimos `nout` iterados del mapeo\n", + "para el valor del parámetro del mapeo `crange[i]`.\n", + "\n", + "La función `f` debe ser definida de tal manera que `f(x0, c)` \n", + "tenga sentido.\n", + "\"\"\"\n", + "function diagbifurc(f, nit, nout, crange)\n", + " xx = Vector{Float64}(nout)\n", + " ff = Array{Float64,2}(nout, length(crange))\n", + " \n", + " for ic in eachindex(crange)\n", + " c = crange[ic]\n", + " ciclosestables!(xx, f, nit, nout, c)\n", + " ff[:,ic] = xx\n", + " end\n", + " \n", + " return ff\n", + "end\n", + "\n", + "doc\"\"\"\n", + " Lyapunov(y, F)\n", + "\n", + "Dado un punto un arreglo que contenga todas las iteraciones bajo $F$ de $x_0$, calcula \n", + "$\\frac{1}{n} \\sum_{i=1}^n \\log\\Big| \\, f'(x_i)\\, \\Big|.$\n", + "\"\"\"\n", + "function Lyapunov(y, F::Function)\n", + " n = length(y)\n", + " l = 0\n", + " \n", + " for i in 1:n\n", + " x = abs((F(xdual(y[i]))).der)\n", + " l = l + log(x)\n", + " \n", + " end\n", + " l/n\n", + "end\n", + "\n", + "doc\"\"\"\n", + " iterado(F,x0,n)\n", + "\n", + "Dado un punto $x_0$, esta funció guarda a todas la iteraciones bajo $F$ en un arreglo.\n", + "\"\"\"\n", + "function iterado(F::Function,x0::Float64,n::Int)\n", + " y = Float64[x0] ##El primer elemento es x_0\n", + " x = x0\n", + " for i in 1:n\n", + " x=F(x) #El valor de x cambia con cada iteración\n", + " push!(y,x) #Este nuevo valor se guarda en el arreglo\n", + " end\n", + " y\n", + "end\n", + "\n", + "\n", + "\n", + "doc\"\"\"\n", + "mapeo_liap_all(crange::FloatRange, Qc::Function, x0::Float64, n = 100000)\n", + "\n", + "Calcula el exponente de Lyapunov para un mapeo paramétrico $Q_c = Q_c(x, c)$ en un rango de parámetros `crange`, un\n", + "valor inicial `x0` y `n` iteraciones.\n", + "\"\"\"\n", + "function mapeo_liap_all(crange::FloatRange, Qc::Function, x0::Float64, n = 100_000)\n", + " mapeo = Float64[]\n", + " \n", + " for i in crange\n", + " Qci(x) = Qc(x,i) \n", + " y = iterado(Qci,x0,n)\n", + " l = Lyapunov(y, Qci)\n", + " if abs(l)" + ] + }, + "execution_count": 7, + "metadata": { + "comm_id": "2a77854a-ac72-4f78-bfb1-098e709b222d", + "reactive": true + }, + "output_type": "execute_result" + } + ], + "source": [ + "@manipulate for M in 0.1:0.1:10, R in 1.1:0.1:10\n", + " m1(x, s) = mapins(x, M, s, R)\n", + " srange = 0:200.0\n", + " map1 = mapeo_liap_all(srange, m1, 1000.0)\n", + " ff = diagbifurc(m1, 300, 10, srange); \n", + " cc = ones(size(ff)[1])*srange';\n", + "\n", + "# Esto cambia las matrices en vectores; ayuda un poco para los dibujos\n", + " ff = reshape(ff, size(ff)[1]*size(ff)[2]);\n", + " cc = reshape(cc, size(ff));\n", + " scatter(cc, ff, markersize= 0.5)\n", + " ylims!(0, 10)\n", + " title!(\"Diagrama de bifurcación para mapeo de poblaciones\")\n", + " xlabel!(L\"S\")\n", + " ylabel!(L\"x_n\")\n", + " #for l in eachindex(ff)\n", + " # if ff[l] == 0\n", + " # @show cc[l]\n", + " # end\n", + " #end\n", + "end" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Ahora revisaremos el tiempo de cálculo usando iteraciones y exponentes de Lypunov y así decidir sobre el más eficiente." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T13:19:12.677803", + "start_time": "2016-12-05T19:19:11.643Z" + }, + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "elapsed time: 0.86598408 seconds\n" + ] + }, + { + "data": { + "text/plain": [ + "0.86598408" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tic()\n", + "M, R = 200, 200\n", + " m1(x, s) = mapins(x, M, s, R)\n", + " srange = 0:9990.0\n", + " #map1 = mapeo_liap_all(srange, m1, 1000.0)\n", + " ff = diagbifurc(m1, 300, 50, srange); \n", + " cc = ones(size(ff)[1])*srange';\n", + "cs = 0\n", + " # Esto cambia las matrices en vectores; ayuda un poco para los dibujos\n", + " ff = reshape(ff, size(ff)[1]*size(ff)[2]);\n", + " cc = reshape(cc, size(ff));\n", + " for l in eachindex(ff)\n", + " if ff[l] == 0\n", + " cs = cc[l]\n", + " break\n", + " end\n", + " end\n", + "cs\n", + "toc()" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T13:24:41.424604", + "start_time": "2016-12-05T19:23:56.834Z" + }, + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "elapsed time: 44.580758861 seconds\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WARNING: Method definition m1(Any, Any) in module Main at In[16]:3 overwritten at In[24]:3.\n" + ] + }, + { + "data": { + "text/plain": [ + "44.580758861" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "tic()\n", + "M, R = 200, 200\n", + " m1(x, s) = mapins(x, M, s, R)\n", + " srange = 0:1000.0\n", + " map1 = mapeo_liap_all(srange, m1, 1000.0)\n", + " #ff = diagbifurc(m1, 300, 50, srange); \n", + " #cc = ones(size(ff)[1])*srange';\n", + " cs = 0\n", + " # Esto cambia las matrices en vectores; ayuda un poco para los dibujos\n", + " #ff = reshape(ff, size(ff)[1]*size(ff)[2]);\n", + " #cc = reshape(cc, size(ff));\n", + " for l in eachindex(srange)\n", + " if map1[l] == 0\n", + " cs = cc[l]\n", + " break\n", + " end\n", + " end\n", + "cs\n", + "toc()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Vemos que el método de Lyapunov es mucho más lento, por lo que usaremos el primero, es decir, iterar muchas veces y buscar el primer valor de $S$ para el cual $x_n = 0$" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-03T12:37:42.728256", + "start_time": "2016-12-03T18:37:42.714Z" + }, + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1.1:0.1:200.0" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "M1 = 1:200\n", + "R1 = 1.1:0.1:200" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T13:12:44.375097", + "start_time": "2016-12-05T19:12:44.322Z" + }, + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WARNING: Method definition iteram(Base.Range, Base.Range) in module Main at In[9]:8 overwritten at In[11]:11.\n", + "WARNING: replacing docs for 'iteram :: Tuple{Range,Range}' in module 'Main'.\n" + ] + }, + { + "data": { + "text/plain": [ + "iteram" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "doc\"\"\"\n", + "`iteram` \n", + "\n", + "Calcula el valor de $S_c$ para el cual las iteraciones del mapeo \n", + "$x_{n + 1} = \\frac{R*x^2}{(R - 1)*(x^2)/M + S + x}$ tienden a cero. \n", + "\n", + "Esto se realiza para los rangos\n", + "$M1 = m_{min}:m_{step}:m_{max}$ y $R1 = r_{min}:r_{step}:r_{max}$. Es necesario que $r_{min} > 1$ y $r_{min} > 0$\n", + "\"\"\"\n", + "function iteram(M1::Range, R1::Range)\n", + " P, Q = length(R1), length(M1)\n", + " Mat1 = zeros(P, Q) \n", + " K = Int(P*Q)\n", + " n = 1\n", + " #@show (P, Q)\n", + " for j in 1:Q\n", + " for i in 1:P\n", + " if mod(100n/K, 10) == 0\n", + " println(100n/K, \"%\")\n", + " end\n", + " #@show i, j\n", + " M, R = M1[j], R1[i]\n", + " m1(x, s) = mapins(x, M, s, R)\n", + " srange = 0:2500.0\n", + " #map1 = mapeo_liap_all(srange, m1, 1000.0)\n", + " ff = diagbifurc(m1, 300, 50, srange); \n", + " cc = ones(size(ff)[1])*srange';\n", + " \n", + " # Esto cambia las matrices en vectores; ayuda un poco para los dibujos\n", + " ff = reshape(ff, size(ff)[1]*size(ff)[2]);\n", + " cc = reshape(cc, size(ff));\n", + " for l in eachindex(ff)\n", + " if ff[l] == 0\n", + " Mat1[i, j] = cc[l]\n", + " break\n", + " end\n", + " end\n", + " n += 1\n", + " end\n", + " end\n", + "\n", + " mm = ones(size(Mat1)[1])*M1'\n", + " rr = R1*ones(size(Mat1)[2])'\n", + " A1 = reshape(Mat1, size(Mat1)[1]*size(Mat1)[2])\n", + " mm1 = reshape(mm, size(A1)[1])\n", + " rr1 = reshape(rr, size(A1)[1])\n", + " return mm1, rr1, A1\n", + "end" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "En la siguiente celda se calcularán las $S_c$'s y se escribirán los datos en archivos `.csv`, pues los calculos son tardados" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-03T19:31:23.972848", + "start_time": "2016-12-03T18:37:54.166Z" + }, + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "10.0%\n", + "20.0%\n", + "30.0%\n", + "40.0%\n", + "50.0%\n", + "60.0%\n", + "70.0%\n", + "80.0%\n", + "90.0%\n", + "100.0%\n" + ] + } + ], + "source": [ + "mm1, rr1, A1 = iteram(M1, R1);\n", + "writecsv(\"mms1.csv\", mm1)\n", + "writecsv(\"rrs1.csv\", rr1)\n", + "writecsv(\"ccs1.csv\", A1)" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T13:26:44.762158", + "start_time": "2016-12-05T19:26:44.735Z" + }, + "collapsed": false + }, + "outputs": [], + "source": [ + "A1 = readcsv(\"../DatosPlano/ccs1.csv\")[:,1]\n", + "rr1 = readcsv(\"../DatosPlano/rrs1.csv\")[:,1];\n", + "mm1 = readcsv(\"../DatosPlano/mms1.csv\")[:,1];" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Primero veamos algunas proyecciones" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T13:17:34.507645", + "start_time": "2016-12-05T19:17:34.102Z" + }, + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/html": [ + "" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plot(rr1, A1)\n", + "title!(L\"$R$ vs $S_c$\")\n", + "xlabel!(L\"R\")\n", + "ylabel!(L\"S_c\")\n", + "#xlims!(80,83)" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T13:26:48.498543", + "start_time": "2016-12-05T19:26:47.963Z" + }, + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/html": [ + "" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plot(mm1, rr1, A1)\n", + "xlabel!(\"M\")\n", + "ylabel!(\"R\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Dado a los tiempo de cálculo, se correrá el código en varias computadoras, el resutado final se mostrará en el trabajo final." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 0.5.0", + "language": "julia", + "name": "julia-0.5" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "0.5.0" + }, + "latex_envs": { + "bibliofile": "biblio.bib", + "cite_by": "apalike", + "current_citInitial": 1, + "eqLabelWithNumbers": true, + "eqNumInitial": 0 + }, + "widgets": { + "state": { + "603df24a-55be-4de5-9dc3-6c3ba5bb6109": { + "views": [ + { + "cell_index": 4 + } + ] + }, + "c97ef275-6cc8-4a79-8b7d-16118417efb9": { + "views": [ + { + "cell_index": 4 + } + ] + }, + "fa235be2-b496-4991-bdbf-a7f81a5e6a15": { + "views": [ + { + "cell_index": 4 + } + ] + }, + "ff137af8-77d1-40c6-bd59-184abfff0375": { + "views": [ + { + "cell_index": 4 + } + ] + } + }, + "version": "1.2.0" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/proys/InsectPopulation/ProyDaniel/ProyDaniel.ipynb b/proys/InsectPopulation/ProyDaniel/ProyDaniel.ipynb new file mode 100644 index 0000000..7a3c8dd --- /dev/null +++ b/proys/InsectPopulation/ProyDaniel/ProyDaniel.ipynb @@ -0,0 +1,907 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-04T23:37:23.090617", + "start_time": "2016-12-05T05:37:15.429Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + " \n", + " \n", + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "Plots.PyPlotBackend()" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "using Plots, Interact, LaTeXStrings\n", + "pyplot()" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-04T23:37:23.190347", + "start_time": "2016-12-05T05:37:15.763Z" + }, + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "intermap (generic function with 1 method)" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "function intermap(M, R)\n", + " m1(x, s) = mapins(x, M, s, R)\n", + " srange = 0:2500.0\n", + " #map1 = mapeo_liap_all(srange, m1, 1000.0)\n", + " ff = diagbifurc(m1, 300, 10, srange); \n", + " cc = ones(size(ff)[1])*srange';\n", + "\n", + "# Esto cambia las matrices en vectores; ayuda un poco para los dibujos\n", + " ff = reshape(ff, size(ff)[1]*size(ff)[2]);\n", + " cc = reshape(cc, size(ff));\n", + " return ff, cc\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-04T23:37:23.301461", + "start_time": "2016-12-05T05:37:16.323Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "iteram (generic function with 1 method)" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "#Código para generar las bifurcaciones\n", + "\"\"\"\n", + " ciclosestables!(xx, f, nit, nout, cc)\n", + "\n", + "Esta función itera el mapeo `f`, de una variable, `nit+nout` veces, \n", + "usando como condición inicial `x0=0`; los últimos `nout` iterados \n", + "actualizan al vector `xx` que tiene longitud `nout`. `cc` es el valor\n", + "del parámetro del mapeo `f`. El mapeo `f` debe ser definido de \n", + "tal manera que `f(x0,cc)` tenga sentido. La idea es los últimos \n", + "`nout` iterados reflejen los ciclos estables del mapeo `f`. \n", + "\"\"\"\n", + "function ciclosestables!(xx, f, nit, nout, cc)\n", + " @assert nit > 0 && nout > 0\n", + " \n", + " # Primeros nit iterados\n", + " x0 = 1000.0\n", + " for it = 1:nit\n", + " x0 = f(x0, cc)\n", + " end\n", + " \n", + " # Se guardan los siguientes nout iterados\n", + " for it = 1:nout\n", + " x0 = f(x0, cc)\n", + " @inbounds xx[it] = x0\n", + " end\n", + " \n", + " nothing\n", + "end\n", + "\"\"\"\n", + " diagbifurc(f, nit, nout, crange)\n", + "\n", + "Itera el mapeo `f` `nit+nout` veces y regresa una matriz\n", + "cuya columna `i` tiene los últimos `nout` iterados del mapeo\n", + "para el valor del parámetro del mapeo `crange[i]`.\n", + "\n", + "La función `f` debe ser definida de tal manera que `f(x0, c)` \n", + "tenga sentido.\n", + "\"\"\"\n", + "function diagbifurc(f, nit, nout, crange)\n", + " xx = Vector{Float64}(nout)\n", + " ff = Array{Float64,2}(nout, length(crange))\n", + " \n", + " for ic in eachindex(crange)\n", + " c = crange[ic]\n", + " ciclosestables!(xx, f, nit, nout, c)\n", + " ff[:,ic] = xx\n", + " end\n", + " \n", + " return ff\n", + "end\n", + "\n", + "doc\"\"\"\n", + " Lyapunov(y, F)\n", + "\n", + "Dado un punto un arreglo que contenga todas las iteraciones bajo $F$ de $x_0$, calcula \n", + "$\\frac{1}{n} \\sum_{i=1}^n \\log\\Big| \\, f'(x_i)\\, \\Big|.$\n", + "\"\"\"\n", + "function Lyapunov(y, F::Function)\n", + " n = length(y)\n", + " l = 0\n", + " \n", + " for i in 1:n\n", + " x = abs((F(xdual(y[i]))).der)\n", + " l = l + log(x)\n", + " \n", + " end\n", + " l/n\n", + "end\n", + "\n", + "doc\"\"\"\n", + " iterado(F,x0,n)\n", + "\n", + "Dado un punto $x_0$, esta funció guarda a todas la iteraciones bajo $F$ en un arreglo.\n", + "\"\"\"\n", + "function iterado(F::Function,x0::Float64,n::Int)\n", + " y = Float64[x0] ##El primer elemento es x_0\n", + " x = x0\n", + " for i in 1:n\n", + " x=F(x) #El valor de x cambia con cada iteración\n", + " push!(y,x) #Este nuevo valor se guarda en el arreglo\n", + " end\n", + " y\n", + "end\n", + "\n", + "\n", + "\n", + "doc\"\"\"\n", + "mapeo_liap_all(crange::FloatRange, Qc::Function, x0::Float64, n = 100000)\n", + "\n", + "Calcula el exponente de Lyapunov para un mapeo paramétrico $Q_c = Q_c(x, c)$ en un rango de parámetros `crange`, un\n", + "valor inicial `x0` y `n` iteraciones.\n", + "\"\"\"\n", + "function mapeo_liap_all(crange::FloatRange, Qc::Function, x0::Float64, n = 100_000)\n", + " mapeo = Float64[]\n", + " \n", + " for i in crange\n", + " Qci(x) = Qc(x,i) \n", + " y = iterado(Qci,x0,n)\n", + " l = Lyapunov(y, Qci)\n", + " if abs(l)" + ] + }, + "execution_count": 5, + "metadata": { + "comm_id": "ac7bd381-e049-4f9b-8b14-a25cc245ef7a", + "reactive": true + }, + "output_type": "execute_result" + } + ], + "source": [ + "@manipulate for M in 1:100, R in 1.1:0.1:100\n", + " ff, cc = intermap(M, R)\n", + " scatter(cc, ff, markersize= 0.5, legend = :false, title =\"Diagrama de bifurcacion\", xlabel =L\"s\", ylabel =L\"x_{300}\")\n", + " xlims!(0, 2500)\n", + " ylims!(0, 100)\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-04T23:37:41.532978", + "start_time": "2016-12-05T05:37:18.995Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [], + "source": [ + "#Parte de Sofia\n", + "#M1 = 1:67\n", + "\n", + "#Parte de Pablo\n", + "#M1 = 68:134\n", + "\n", + "#Parte de Daniel\n", + "#M1 = 67:100\n", + "\n", + "#R1 = 1.1:0.1:100" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-04T23:37:41.536148", + "start_time": "2016-12-05T05:37:19.435Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [], + "source": [ + "#Parte de Sofía\n", + "#mm1, rr1, A1 = iteram(M1, R1);\n", + "#writecsv(\"mms1.csv\", mm1)\n", + "#writecsv(\"rrs1.csv\", rr1)\n", + "#writecsv(\"ccs1.csv\", A1)\n", + "\n", + "\n", + "#Parte de Pablo\n", + "#mm2, rr2, A2 = iteram(M1, R1);\n", + "#writecsv(\"mms2.csv\", mm2)\n", + "#writecsv(\"rrs2.csv\", rr2)\n", + "#writecsv(\"ccs2.csv\", A2)\n", + "\n", + "#Parte de Daniel\n", + "\n", + "#mm3, rr3, A3 = iteram(M1, R1);\n", + "#writecsv(\"mms3.csv\", mm3)\n", + "#writecsv(\"rrs3.csv\", rr3)\n", + "#writecsv(\"ccs3.csv\", A3)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "Lo siguiente fue encotrar $S_c$ como función de $M$ y $R$, para esto empleamos el dominio $M\\times R = [1,100]\\times[1.1,100]$" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-04T23:37:43.348339", + "start_time": "2016-12-05T05:37:25.044Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [], + "source": [ + "mm = readcsv(\"DatosPlano/mms2.csv\")[:,1]\n", + "rr = readcsv(\"DatosPlano/rrs2.csv\")[:,1]\n", + "cs = readcsv(\"DatosPlano/ccs2.csv\")[:,1];\n", + "append!(mm, readcsv(\"DatosPlano/mms3.csv\")[:,1])\n", + "append!(rr, readcsv(\"DatosPlano/rrs3.csv\")[:,1])\n", + "append!(cs, readcsv(\"DatosPlano/ccs3.csv\")[:,1]);\n", + "append!(mm, readcsv(\"DatosPlano/mms1.csv\")[:,1])\n", + "append!(rr, readcsv(\"DatosPlano/rrs1.csv\")[:,1])\n", + "append!(cs, readcsv(\"DatosPlano/ccs1.csv\")[:,1]);" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-04T23:38:23.001597", + "start_time": "2016-12-05T05:37:52.090Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "slide" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plot(mm, rr, cs, st = :surface)\n", + "xlabel!(\"M\")\n", + "ylabel!(\"R\")" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-04T23:40:55.547125", + "start_time": "2016-12-05T05:40:52.909Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + " \n", + "

Plotly javascript loaded.

\n", + "

To load again call

init_notebook(true)

\n", + " " + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "Plots.PlotlyJSBackend()" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "using Plots\n", + "plotlyjs()" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-04T23:40:57.380825", + "start_time": "2016-12-05T05:40:53.891Z" + }, + "collapsed": true, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [], + "source": [ + "mm = readcsv(\"DatosPlano/mms2.csv\")[:,1]\n", + "rr = readcsv(\"DatosPlano/rrs2.csv\")[:,1]\n", + "cs = readcsv(\"DatosPlano/ccs2.csv\")[:,1];\n", + "append!(mm, readcsv(\"DatosPlano/mms3.csv\")[:,1])\n", + "append!(rr, readcsv(\"DatosPlano/rrs3.csv\")[:,1])\n", + "append!(cs, readcsv(\"DatosPlano/ccs3.csv\")[:,1]);\n", + "append!(mm, readcsv(\"DatosPlano/mms1.csv\")[:,1])\n", + "append!(rr, readcsv(\"DatosPlano/rrs1.csv\")[:,1])\n", + "append!(cs, readcsv(\"DatosPlano/ccs1.csv\")[:,1]);" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-04T23:41:11.272203", + "start_time": "2016-12-05T05:40:55.352Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "slide" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + " \n", + "\n", + "\n", + "
\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plot(mm, rr, cs)\n", + "xlabel!(\"M\")\n", + "ylabel!(\"R\")" + ] + } + ], + "metadata": { + "celltoolbar": "Slideshow", + "kernelspec": { + "display_name": "Julia 0.5.0", + "language": "julia", + "name": "julia-0.5" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "0.5.0" + }, + "latex_envs": { + "bibliofile": "biblio.bib", + "cite_by": "apalike", + "current_citInitial": 1, + "eqLabelWithNumbers": true, + "eqNumInitial": 0 + }, + "widgets": { + "state": { + "016118e6-7893-4f00-af84-3af6c9eda509": { + "views": [ + { + "cell_index": 5 + } + ] + }, + "2b4434be-7b6b-4df3-ad70-dab8658a5499": { + "views": [ + { + "cell_index": 5 + } + ] + }, + "409c09cc-6a50-44eb-ba68-ca230f32868f": { + "views": [ + { + "cell_index": 5 + } + ] + }, + "86393c53-2969-4873-bf86-7fc248790cd5": { + "views": [ + { + "cell_index": 5 + } + ] + }, + "ad32d8d3-a6d7-48bf-b407-588a5da06684": { + "views": [ + { + "cell_index": 5 + } + ] + }, + "fb4909b9-c2a1-41b0-ada0-0fe564fb9fbc": { + "views": [ + { + "cell_index": 5 + } + ] + } + }, + "version": "1.2.0" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/proys/InsectPopulation/ProySofi/Proyecciones.ipynb b/proys/InsectPopulation/ProySofi/Proyecciones.ipynb new file mode 100644 index 0000000..02efbae --- /dev/null +++ b/proys/InsectPopulation/ProySofi/Proyecciones.ipynb @@ -0,0 +1,1356 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "using Plots, LaTeXStrings, TaylorSeries\n", + "include(\"AutomDiff_V2.jl\")\n", + "import AD: Dual, xdual\n", + "#pyplot(grid=:false, size=(400,267))" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "ciclosestables!" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "\"\"\"\n", + " ciclosestables!(xx, f, nit, nout, cc)\n", + "\n", + "Esta función itera el mapeo `f`, de una variable, `nit+nout` veces, \n", + "usando como condición inicial `x0=0`; los últimos `nout` iterados \n", + "actualizan al vector `xx` que tiene longitud `nout`. `cc` es el valor\n", + "del parámetro del mapeo `f`. El mapeo `f` debe ser definido de \n", + "tal manera que `f(x0,cc)` tenga sentido. La idea es los últimos \n", + "`nout` iterados reflejen los ciclos estables del mapeo `f`. \n", + "\"\"\"\n", + "function ciclosestables!(xx, f, nit, nout, cc,x0)\n", + " @assert nit > 0 && nout > 0\n", + " \n", + " # Primeros nit iterados\n", + " \n", + " for it = 1:nit\n", + " x0 = f(x0, cc)\n", + " end\n", + " \n", + " # Se guardan los siguientes nout iterados\n", + " for it = 1:nout\n", + " x0 = f(x0, cc)\n", + " @inbounds xx[it] = x0\n", + " end\n", + " \n", + " nothing\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "diagbifurc" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "\"\"\"\n", + " diagbifurc(f, nit, nout, crange)\n", + "\n", + "Itera el mapeo `f` `nit+nout` veces y regresa una matriz\n", + "cuya columna `i` tiene los últimos `nout` iterados del mapeo\n", + "para el valor del parámetro del mapeo `crange[i]`.\n", + "\n", + "La función `f` debe ser definida de tal manera que `f(x0, c)` \n", + "tenga sentido.\n", + "\"\"\"\n", + "function diagbifurc(f, nit, nout, crange,x0)\n", + " xx = Vector{Float64}(nout)\n", + " ff = Array{Float64,2}(nout, length(crange))\n", + " \n", + " for ic in eachindex(crange)\n", + " c = crange[ic]\n", + " ciclosestables!(xx, f, nit, nout, c,x0)\n", + " ff[:,ic] = xx\n", + " end\n", + " \n", + " return ff\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "Ict(x,m, r,s) = (r*x^2)/((r-1)*x^2/m + x + s)\n", + "\n", + "M=63\n", + "R=20\n", + "Ict1(x,s) = Ict(x,M,R,s)\n", + "\n", + "crange = 0:1000\n", + "\n", + "ff = diagbifurc(Ict1, 1000, 256, crange,50); \n", + "cc = ones(size(ff)[1])*crange';\n", + "\n", + "# Esto cambia las matrices en vectores; ayuda un poco para los dibujos\n", + "ff = reshape(ff, size(ff)[1]*size(ff)[2]);\n", + "cc = reshape(cc, size(ff));" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/html": [ + "" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "scatter(cc, ff, markersize= 0.05)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/sof9409/anaconda/lib/python2.7/site-packages/matplotlib/font_manager.py:1288: UserWarning: findfont: Font family [u'Helvetica'] not found. Falling back to Bitstream Vera Sans\n", + " (prop.get_family(), self.defaultFamily[fontext]))\n" + ] + }, + { + "data": { + "text/plain": [ + "1-element Array{Float64,1}:\n", + " 300.0" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "n = length(cc)\n", + "sc=Float64[]\n", + "for i in 1:n\n", + " if ff[i]==0.0\n", + " push!(sc,cc[i])\n", + " \n", + " break\n", + " end\n", + "end\n", + "sc" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "mapeo_liap_all" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "doc\"\"\"\n", + " iterado(F,x0,n)\n", + "\n", + "Dado un punto $x_0$, esta funció guarda a todas la iteraciones bajo $F$ en un arreglo.\n", + "\"\"\"\n", + "\n", + "function iterado(F::Function,x0::Float64,n::Int)\n", + " y = Float64[x0] ##El primer elemento es x_0\n", + " x = x0\n", + " for i in 1:n\n", + " x=F(x) #El valor de x cambia con cada iteración\n", + " push!(y,x) #Este nuevo valor se guarda en el arreglo\n", + " end\n", + " y\n", + "end\n", + "\n", + "doc\"\"\"\n", + " Lyapunov(y, F)\n", + "\n", + "Dado un punto un arreglo que contenga todas las iteraciones bajo $F$ de $x_0$, calcula \n", + "$\\frac{1}{n} \\sum_{i=1}^n \\log\\Big| \\, f'(x_i)\\, \\Big|.$\n", + "\"\"\"\n", + "\n", + "function Lyapunov(y, F::Function)\n", + " n = length(y)\n", + " l = 0\n", + " \n", + " for i in 1:n\n", + " x = abs((F(xdual(y[i]))).der)\n", + " l = l + log(x)\n", + " \n", + " end\n", + " l/n\n", + "end\n", + "\n", + "doc\"\"\"\n", + "mapeo_liap_all(crange::FloatRange, Qc::Function, x0::Float64, n = 100000)\n", + "\n", + "Calcula el exponente de Lyapunov para un mapeo paramétrico $Q_c = Q_c(x, c)$ en un rango de parámetros `crange`, un\n", + "valor inicial `x0` y `n` iteraciones.\n", + "\"\"\"\n", + "\n", + "function mapeo_liap_all(crange::FloatRange, Qc::Function, x0::Float64, n = 100000)\n", + " mapeo = Float64[]\n", + " \n", + " for i in crange\n", + " Qci(x) = Qc(x,i) \n", + " y = iterado(Qci,x0,n)\n", + " l = Lyapunov(y, Qci)\n", + " if abs(l)" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "p = plot(crange,mapeo)\n", + "\n", + "xlabel!(L\"c\")\n", + "ylabel!(L\"\\lambda\")\n", + "title!(L\"Exponente de Lyapunov $Q_c = x^2 +c$\")" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1-element Array{Float64,1}:\n", + " 299.5" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "n = length(crange)\n", + "sc=Float64[]\n", + "for i in 1:n\n", + " if mapeo[i]==0.0\n", + " push!(sc,(crange[i-1]+crange[i])/2)\n", + " \n", + " break\n", + " end\n", + "end\n", + "sc" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WARNING: Method definition Ict(Any, Any, Any, Any) in module Main at In[4]:1 overwritten at In[11]:1.\n", + "WARNING: Method definition Ict1(Any, Any) in module Main at In[4]:5 overwritten at In[11]:5.\n" + ] + }, + { + "data": { + "text/plain": [ + "1-element Array{Float64,1}:\n", + " 300.0" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Ict(x,m, r,s) = (r*x^2)/((r-1)*x^2/m + x + s)\n", + "\n", + "M=63\n", + "R=20\n", + "Ict1(x,s) = Ict(x,M,R,s)\n", + "\n", + "crange = 0:1000\n", + "\n", + "ff = diagbifurc(Ict1, 1000, 256, crange,50); \n", + "cc = ones(size(ff)[1])*crange';\n", + "\n", + "# Esto cambia las matrices en vectores; ayuda un poco para los dibujos\n", + "ff = reshape(ff, size(ff)[1]*size(ff)[2]);\n", + "cc = reshape(cc, size(ff));\n", + "\n", + "n = length(cc)\n", + "sc=Float64[]\n", + "for i in 1:n\n", + " if ff[i]==0.0\n", + " push!(sc,cc[i])\n", + " break\n", + " end\n", + "end\n", + "sc" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "SC (generic function with 1 method)" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "function SC(Mrange,Rrange)\n", + " R = length(Rrange)\n", + " Mmax = length(Mrange)\n", + " M = zeros(Mmax,R)\n", + " crange = 0:1000\n", + " for i in 1:Mmax\n", + " for j in 1:R\n", + " I(x,s) = Ict(x,Mrange[i],Rrange[j],s)\n", + " \n", + " ff = diagbifurc(I, 1000, 256, crange,100); \n", + " cc = ones(size(ff)[1])*crange';\n", + " \n", + " if mod(j,10) == 0\n", + " @show(j,i)\n", + " end\n", + " \n", + " n = length(cc)\n", + " for k in 1:n\n", + " if ff[k]==0.0\n", + " M[i,j]= cc[k]\n", + " break\n", + " end\n", + " end\n", + " end\n", + " end\n", + " M\n", + "end\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "j = 10\n", + "i = 1\n", + "j = 10\n", + "i = 2\n", + "j = 10\n", + "i = 3\n", + "j = 10\n", + "i = 4\n", + "j = 10\n", + "i = 5\n", + "j = 10\n", + "i = 6\n", + "j = 10\n", + "i = 7\n", + "j = 10\n", + "i = 8\n", + "j = 10\n", + "i = 9\n", + "j = 10\n", + "i = 10\n", + "j = 10\n", + "i = 11\n", + "j = 10\n", + "i = 12\n", + "j = 10\n", + "i = 13\n", + "j = 10\n", + "i = 14\n", + "j = 10\n", + "i = 15\n", + "j = 10\n", + "i = 16\n", + "j = 10\n", + "i = 17\n", + "j = 10\n", + "i = 18\n", + "j = 10\n", + "i = 19\n", + "j = 10\n", + "i = 20\n", + "j = 10\n", + "i = 21\n", + "j = 10\n", + "i = 22\n", + "j = 10\n", + "i = 23\n", + "j = 10\n", + "i = 24\n", + "j = 10\n", + "i = 25\n", + "j = 10\n", + "i = 26\n", + "j = 10\n", + "i = 27\n", + "j = 10\n", + "i = 28\n", + "j = 10\n", + "i = 29\n", + "j = 10\n", + "i = 30\n", + "j = 10\n", + "i = 31\n", + "j = 10\n", + "i = 32\n", + "j = 10\n", + "i = 33\n", + "j = 10\n", + "i = 34\n", + "j = 10\n", + "i = 35\n", + "j = 10\n", + "i = 36\n", + "j = 10\n", + "i = 37\n", + "j = 10\n", + "i = 38\n", + "j = 10\n", + "i = 39\n", + "j = 10\n", + "i = 40\n", + "j = 10\n", + "i = 41\n", + "j = 10\n", + "i = 42\n", + "j = 10\n", + "i = 43\n", + "j = 10\n", + "i = 44\n", + "j = 10\n", + "i = 45\n", + "j = 10\n", + "i = 46\n", + "j = 10\n", + "i = 47\n", + "j = 10\n", + "i = 48\n", + "j = 10\n", + "i = 49\n", + "j = 10\n", + "i = 50\n", + "j = 10\n", + "i = 51\n", + "j = 10\n", + "i = 52\n", + "j = 10\n", + "i = 53\n", + "j = 10\n", + "i = 54\n", + "j = 10\n", + "i = 55\n", + "j = 10\n", + "i = 56\n", + "j = 10\n", + "i = 57\n", + "j = 10\n", + "i = 58\n", + "j = 10\n", + "i = 59\n", + "j = 10\n", + "i = 60\n", + "j = 10\n", + "i = 61\n", + "j = 10\n", + "i = 62\n", + "j = 10\n", + "i = 63\n", + "j = 10\n", + "i = 64\n", + "j = 10\n", + "i = 65\n", + "j = 10\n", + "i = 66\n", + "j = 10\n", + "i = 67\n", + "j = 10\n", + "i = 68\n", + "j = 10\n", + "i = 69\n", + "j = 10\n", + "i = 70\n", + "j = 10\n", + "i = 71\n", + "j = 10\n", + "i = 72\n", + "j = 10\n", + "i = 73\n", + "j = 10\n", + "i = 74\n", + "j = 10\n", + "i = 75\n", + "j = 10\n", + "i = 76\n", + "j = 10\n", + "i = 77\n", + "j = 10\n", + "i = 78\n", + "j = 10\n", + "i = 79\n", + "j = 10\n", + "i = 80\n", + "j = 10\n", + "i = 81\n", + "j = 10\n", + "i = 82\n", + "j = 10\n", + "i = 83\n", + "j = 10\n", + "i = 84\n", + "j = 10\n", + "i = 85\n", + "j = 10\n", + "i = 86\n", + "j = 10\n", + "i = 87\n", + "j = 10\n", + "i = 88\n", + "j = 10\n", + "i = 89\n", + "j = 10\n", + "i = 90\n", + "j = 10\n", + "i = 91\n", + "j = 10\n", + "i = 92\n", + "j = 10\n", + "i = 93\n", + "j = 10\n", + "i = 94\n", + "j = 10\n", + "i = 95\n", + "j = 10\n", + "i = 96\n", + "j = 10\n", + "i = 97\n", + "j = 10\n", + "i = 98\n", + "j = 10\n", + "i = 99\n", + "j = 10\n", + "i = 100\n" + ] + }, + { + "data": { + "text/plain": [ + "100×17 Array{Float64,2}:\n", + " 1.0 1.0 1.0 1.0 1.0 1.0 1.0 … 1.0 1.0 1.0 1.0 2.0\n", + " 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 3.0\n", + " 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 4.0\n", + " 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 4.0 5.0\n", + " 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 5.0 6.0\n", + " 6.0 6.0 6.0 6.0 6.0 6.0 6.0 … 6.0 6.0 6.0 6.0 7.0\n", + " 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 7.0 8.0\n", + " 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 8.0 9.0\n", + " 8.0 8.0 9.0 9.0 9.0 9.0 9.0 9.0 9.0 9.0 9.0 10.0\n", + " 9.0 9.0 9.0 9.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 11.0\n", + " 10.0 10.0 10.0 10.0 10.0 11.0 11.0 … 11.0 11.0 11.0 11.0 12.0\n", + " 11.0 11.0 11.0 11.0 11.0 11.0 12.0 12.0 12.0 12.0 12.0 13.0\n", + " 12.0 12.0 12.0 12.0 12.0 12.0 12.0 13.0 13.0 13.0 13.0 14.0\n", + " ⋮ ⋮ ⋱ ⋮ \n", + " 78.0 79.0 80.0 80.0 81.0 82.0 83.0 87.0 87.0 88.0 89.0 90.0\n", + " 79.0 80.0 81.0 81.0 82.0 83.0 83.0 88.0 88.0 89.0 90.0 91.0\n", + " 80.0 81.0 82.0 82.0 83.0 84.0 84.0 … 89.0 89.0 90.0 91.0 92.0\n", + " 81.0 82.0 82.0 83.0 84.0 85.0 85.0 90.0 90.0 91.0 92.0 93.0\n", + " 82.0 83.0 83.0 84.0 85.0 86.0 86.0 91.0 91.0 92.0 93.0 94.0\n", + " 83.0 83.0 84.0 85.0 86.0 86.0 87.0 92.0 92.0 93.0 94.0 95.0\n", + " 84.0 84.0 85.0 86.0 87.0 87.0 88.0 93.0 93.0 94.0 95.0 96.0\n", + " 85.0 85.0 86.0 87.0 88.0 88.0 89.0 … 94.0 94.0 95.0 96.0 97.0\n", + " 85.0 86.0 87.0 88.0 88.0 89.0 90.0 94.0 95.0 96.0 97.0 98.0\n", + " 86.0 87.0 88.0 89.0 89.0 90.0 91.0 95.0 96.0 97.0 98.0 99.0\n", + " 87.0 88.0 89.0 89.0 90.0 91.0 92.0 96.0 97.0 98.0 99.0 100.0\n", + " 88.0 89.0 90.0 90.0 91.0 92.0 93.0 97.0 98.0 99.0 100.0 101.0" + ] + }, + "execution_count": 36, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Rrange = 4.5:1/2^5:5\n", + "M=SC(1:100,Rrange)" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/html": [ + "" + ] + }, + "execution_count": 45, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plot(M[:,end-1:end])" + ] + }, + { + "cell_type": "code", + "execution_count": 115, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "j = 10\n", + "i = 1\n", + "j = 20\n", + "i = 1\n", + "j = 30\n", + "i = 1\n", + "j = 10\n", + "i = 2\n", + "j = 20\n", + "i = 2\n", + "j = 30\n", + "i = 2\n", + "j = 10\n", + "i = 3\n", + "j = 20\n", + "i = 3\n", + "j = 30\n", + "i = 3\n", + "j = 10\n", + "i = 4\n", + "j = 20\n", + "i = 4\n", + "j = 30\n", + "i = 4\n", + "j = 10\n", + "i = 5\n", + "j = 20\n", + "i = 5\n", + "j = 30\n", + "i = 5\n", + "j = 10\n", + "i = 6\n", + "j = 20\n", + "i = 6\n", + "j = 30\n", + "i = 6\n", + "j = 10\n", + "i = 7\n", + "j = 20\n", + "i = 7\n", + "j = 30\n", + "i = 7\n", + "j = 10\n", + "i = 8\n", + "j = 20\n", + "i = 8\n", + "j = 30\n", + "i = 8\n", + "j = 10\n", + "i = 9\n", + "j = 20\n", + "i = 9\n", + "j = 30\n", + "i = 9\n", + "j = 10\n", + "i = 10\n", + "j = 20\n", + "i = 10\n", + "j = 30\n", + "i = 10\n", + "j = 10\n", + "i = 11\n", + "j = 20\n", + "i = 11\n", + "j = 30\n", + "i = 11\n", + "j = 10\n", + "i = 12\n", + "j = 20\n", + "i = 12\n", + "j = 30\n", + "i = 12\n", + "j = 10\n", + "i = 13\n", + "j = 20\n", + "i = 13\n", + "j = 30\n", + "i = 13\n", + "j = 10\n", + "i = 14\n", + "j = 20\n", + "i = 14\n", + "j = 30\n", + "i = 14\n", + "j = 10\n", + "i = 15\n", + "j = 20\n", + "i = 15\n", + "j = 30\n", + "i = 15\n", + "j = 10\n", + "i = 16\n", + "j = 20\n", + "i = 16\n", + "j = 30\n", + "i = 16\n", + "j = 10\n", + "i = 17\n", + "j = 20\n", + "i = 17\n", + "j = 30\n", + "i = 17\n", + "j = 10\n", + "i = 18\n", + "j = 20\n", + "i = 18\n", + "j = 30\n", + "i = 18\n", + "j = 10\n", + "i = 19\n", + "j = 20\n", + "i = 19\n", + "j = 30\n", + "i = 19\n", + "j = 10\n", + "i = 20\n", + "j = 20\n", + "i = 20\n", + "j = 30\n", + "i = 20\n", + "j = 10\n", + "i = 21\n", + "j = 20\n", + "i = 21\n", + "j = 30\n", + "i = 21\n", + "j = 10\n", + "i = 22\n", + "j = 20\n", + "i = 22\n", + "j = 30\n", + "i = 22\n", + "j = 10\n", + "i = 23\n", + "j = 20\n", + "i = 23\n", + "j = 30\n", + "i = 23\n", + "j = 10\n", + "i = 24\n", + "j = 20\n", + "i = 24\n", + "j = 30\n", + "i = 24\n", + "j = 10\n", + "i = 25\n", + "j = 20\n", + "i = 25\n", + "j = 30\n", + "i = 25\n", + "j = 10\n", + "i = 26\n", + "j = 20\n", + "i = 26\n", + "j = 30\n", + "i = 26\n", + "j = 10\n", + "i = 27\n", + "j = 20\n", + "i = 27\n", + "j = 30\n", + "i = 27\n", + "j = 10\n", + "i = 28\n", + "j = 20\n", + "i = 28\n", + "j = 30\n", + "i = 28\n", + "j = 10\n", + "i = 29\n", + "j = 20\n", + "i = 29\n", + "j = 30\n", + "i = 29\n", + "j = 10\n", + "i = 30\n", + "j = 20\n", + "i = 30\n", + "j = 30\n", + "i = 30\n", + "j = 10\n", + "i = 31\n", + "j = 20\n", + "i = 31\n", + "j = 30\n", + "i = 31\n", + "j = 10\n", + "i = 32\n", + "j = 20\n", + "i = 32\n", + "j = 30\n", + "i = 32\n", + "j = 10\n", + "i = 33\n", + "j = 20\n", + "i = 33\n", + "j = 30\n", + "i = 33\n", + "j = 10\n", + "i = 34\n", + "j = 20\n", + "i = 34\n", + "j = 30\n", + "i = 34\n", + "j = 10\n", + "i = 35\n", + "j = 20\n", + "i = 35\n", + "j = 30\n", + "i = 35\n", + "j = 10\n", + "i = 36\n", + "j = 20\n", + "i = 36\n", + "j = 30\n", + "i = 36\n", + "j = 10\n", + "i = 37\n", + "j = 20\n", + "i = 37\n", + "j = 30\n", + "i = 37\n", + "j = 10\n", + "i = 38\n", + "j = 20\n", + "i = 38\n", + "j = 30\n", + "i = 38\n", + "j = 10\n", + "i = 39\n", + "j = 20\n", + "i = 39\n", + "j = 30\n", + "i = 39\n", + "j = 10\n", + "i = 40\n", + "j = 20\n", + "i = 40\n", + "j = 30\n", + "i = 40\n", + "j = 10\n", + "i = 41\n", + "j = 20\n", + "i = 41\n", + "j = 30\n", + "i = 41\n", + "j = 10\n", + "i = 42\n", + "j = 20\n", + "i = 42\n", + "j = 30\n", + "i = 42\n", + "j = 10\n", + "i = 43\n", + "j = 20\n", + "i = 43\n", + "j = 30\n", + "i = 43\n", + "j = 10\n", + "i = 44\n", + "j = 20\n", + "i = 44\n", + "j = 30\n", + "i = 44\n", + "j = 10\n", + "i = 45\n", + "j = 20\n", + "i = 45\n", + "j = 30\n", + "i = 45\n", + "j = 10\n", + "i = 46\n", + "j = 20\n", + "i = 46\n", + "j = 30\n", + "i = 46\n", + "j = 10\n", + "i = 47\n", + "j = 20\n", + "i = 47\n", + "j = 30\n", + "i = 47\n", + "j = 10\n", + "i = 48\n", + "j = 20\n", + "i = 48\n", + "j = 30\n", + "i = 48\n", + "j = 10\n", + "i = 49\n", + "j = 20\n", + "i = 49\n", + "j = 30\n", + "i = 49\n", + "j = 10\n", + "i = 50\n", + "j = 20\n", + "i = 50\n", + "j = 30\n", + "i = 50\n" + ] + }, + { + "data": { + "text/plain": [ + "50×36 Array{Float64,2}:\n", + " 2.0 2.0 2.0 2.0 3.0 3.0 … 9.0 10.0 10.0 10.0 10.0\n", + " 3.0 3.0 4.0 4.0 5.0 5.0 18.0 19.0 19.0 20.0 20.0\n", + " 4.0 4.0 5.0 6.0 7.0 7.0 27.0 28.0 28.0 29.0 30.0\n", + " 5.0 6.0 7.0 8.0 9.0 10.0 36.0 37.0 38.0 39.0 40.0\n", + " 6.0 7.0 8.0 9.0 11.0 12.0 44.0 46.0 47.0 48.0 49.0\n", + " 7.0 8.0 10.0 11.0 13.0 14.0 … 53.0 55.0 56.0 58.0 59.0\n", + " 8.0 9.0 11.0 13.0 15.0 16.0 62.0 64.0 65.0 67.0 69.0\n", + " 9.0 11.0 13.0 15.0 17.0 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72.0 83.0 93.0 … 359.0 370.0 380.0 390.0 400.0\n", + " 43.0 53.0 64.0 74.0 85.0 95.0 368.0 379.0 389.0 400.0 410.0\n", + " 44.0 54.0 65.0 76.0 87.0 97.0 377.0 388.0 398.0 409.0 420.0\n", + " 45.0 56.0 67.0 78.0 89.0 100.0 386.0 397.0 408.0 419.0 430.0\n", + " 46.0 57.0 68.0 79.0 91.0 102.0 394.0 406.0 417.0 428.0 439.0\n", + " 47.0 58.0 70.0 81.0 93.0 104.0 … 403.0 415.0 426.0 438.0 449.0\n", + " 48.0 59.0 71.0 83.0 95.0 106.0 412.0 424.0 435.0 447.0 459.0\n", + " 49.0 61.0 73.0 85.0 97.0 109.0 421.0 433.0 445.0 457.0 469.0\n", + " 50.0 62.0 74.0 86.0 99.0 111.0 429.0 442.0 454.0 466.0 478.0\n", + " 51.0 63.0 76.0 88.0 101.0 113.0 438.0 451.0 463.0 476.0 488.0" + ] + }, + "execution_count": 118, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "MS = readcsv(\"M1.csv\")" + ] + }, + { + "cell_type": "code", + "execution_count": 140, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "([5.0,9.0,13.0,17.0,21.0,25.0,29.0,33.0,37.0],[1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0,9.0])" + ] + }, + "execution_count": 140, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "dif=MS\n", + " for j in 1:length(M1[:,1])-1 #fixed m\n", + " dif[j,:]= M1[j+1,:]-M1[j,:]\n", + "end\n", + "\n", + "dif\n", + "dif[end,:]= dif[end-1,:]\n", + "steadyR = Float64[]\n", + "steapR = Float64[]\n", + "for i in 1:36\n", + " u = unique(dif[:,i])\n", + " if length(u)==1\n", + " push!(steadyR,Rrange[i])\n", + " push!(steapR,u[1])\n", + " end\n", + "end\n", + "steadyR,steapR" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "([4.0,8.0,12.0,16.0,20.0,24.0,28.0,32.0,36.0,40.0,44.0,48.0],[1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0,9.0,10.0,11.0,12.0])" + ] + }, + "execution_count": 141, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "dif2=MS\n", + " for j in 1:length(M1[1,:])-1 #fixed m\n", + " dif2[:,j]= M1[:,j+1]-M1[:,j]\n", + "end\n", + "\n", + "dif2\n", + "dif[:,end]= dif[:,end-1]\n", + "steadyM = Float64[]\n", + "steapM = Float64[]\n", + "for i in 1:50\n", + " u = unique(dif[i,:])\n", + " if length(unique(dif[i,:]))==1\n", + " push!(steadyM,i)\n", + " push!(steapM,u[1])\n", + " end\n", + "end\n", + "steadyM,steapM" + ] + }, + { + "cell_type": "code", + "execution_count": 126, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "ename": "LoadError", + "evalue": "LoadError: MethodError: Cannot `convert` an object of type Int64 to an object of type Range{T}\nThis may have arisen from a call to the constructor Range{T}(...),\nsince type constructors fall back to convert methods.\nwhile loading In[126], in expression starting on line 1", + "output_type": "error", + "traceback": [ + "LoadError: MethodError: Cannot `convert` an object of type Int64 to an object of type Range{T}\nThis may have arisen from a call to the constructor Range{T}(...),\nsince type constructors fall back to convert methods.\nwhile loading In[126], in expression starting on line 1", + "", + " in getindex(::Type{Range}, ::Int64) at ./array.jl:138" + ] + } + ], + "source": [ + "unique(dif[:,1])" + ] + }, + { + "cell_type": "code", + "execution_count": 99, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/html": [ + "" + ] + }, + "execution_count": 99, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "scatter(M1[1,:])\n", + "scatter!(M1[2,:])\n", + "scatter!(M1[3,:])\n", + "scatter!(M1[4,:])" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1×8 Array{Float64,2}:\n", + " 1.0 9.0 16.0 24.0 31.0 39.0 46.0 54.0" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Rrange = 1+1/2^2:2:16\n", + "M2=SC(15,Rrange)" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "3-element Array{Int64,1}:\n", + " 1\n", + " 2\n", + " 3" + ] + }, + "execution_count": 61, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "unique([1,1,2,3])" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 0.5.0", + "language": "julia", + "name": "julia-0.5" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "0.5.0" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/proys/InsectPopulation/README.md b/proys/InsectPopulation/README.md new file mode 100644 index 0000000..3465107 --- /dev/null +++ b/proys/InsectPopulation/README.md @@ -0,0 +1,22 @@ +# Proyecto: *Modelos discretos de control de poblaciones de insectos al introducir insectos estériles* + +===================== + +## Autores: + +- Sofía Cruz T. (**@cutsof**) + +- Daniel Martínez U.(**@danmarurr**) + +- Pablo Reséndiz V. (**@Pablorv**) + + +===================== + + +En este proyecto se estudia el mapeo que modela el control de poblaciones de insectos mediante la inserción de `S` insectos estériles. Dicho mapeo está dado por: + +![Mapeo de control](Figures/equation.png) + +donde `R` y `M` son parámetros que controlan la rapidez de crecimiento de población y el valor de población final respectivamente. + diff --git a/proys/InsectPopulation/TrabajoFinal.ipynb b/proys/InsectPopulation/TrabajoFinal.ipynb new file mode 100644 index 0000000..66b20ca --- /dev/null +++ b/proys/InsectPopulation/TrabajoFinal.ipynb @@ -0,0 +1,2046 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "# Control de Poblaciones de Insectos al Introducir Insectos Estériles\n", + "\n", + "\\ \n", + "\\\n", + "\n", + "\n", + "
Sofía Cruz T.
\n", + "
Daniel Martínez U.
\n", + "
Pablo Reśendiz V.
\n", + "\n", + "$$\n", + "N_{t+1}=\\frac{R N_t^2}{(R-1)\\frac{N_t^2}{M}+N_t+S}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "En 1937, E. F. Knipling, propuso la Técnica de Insectos Estériles (SIT, en inglés). La técnica no fue implementada haste 1958 sobre una plaga de `screwworm` en EEUU usando métodos físicos y químicos para causar esterilidad. El método ha sido implementado en México y otros países de Sudamérica con éxito.\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "Hasta años recientes SIT sigue siendo una técnica usada y estudiada en genética de poblaciones\n", + "\n", + "* `Oliva, C., Damiens, D., Vreysen, M., Lempeiere, G., & Gilles, J. (2013). Reproductive strategies of aedes albopictus (diptera: Culicidae) and implications for the sterile insect technique. Plos One, 8(11), e78884. doi:10.1371/journal.pone.0078884`" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "* `Barnes, B. N., Hofmeyr, J. H., Groenewald, S., Conlong, D. E., & Wohlfarter, M. (2015). The sterile insect technique in agricultural crops in south africa: A metamorphosis …. but will it fly? African Entomology, 23(1), 1-18. doi:10.4001/003.023.0103`\n", + "\n", + "* `Horner, R. M., Walker, J. T. S., Rogers, D. J., Lo, P. L., & Suckling, D. M. (2016). Use of the sterile insect technique in new zealand: Benefits and constraints. New Zealand Plant Protection, 69, 296-304.`\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "\n", + "Basándonos en la ecuación propuesta por `Murray, J. D. (2001). Mathematical biology, part I: An introduction Springer.` Nuestra ecuación tenemos varios parámetros:\n", + "\n", + "+ $N_t$ población al tiempo $t$\n", + "+ R Rapidez de crecimiento\n", + "+ S Número constante de individuos estériles\n", + "+ M Población convergente si $S=0$" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T01:07:43.102140", + "start_time": "2016-12-05T07:07:34.862Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + " \n", + " \n", + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "Plots.PyPlotBackend()" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "using Plots, LaTeXStrings, TaylorSeries, Interact\n", + "include(\"AutomDiff_V2.jl\")\n", + "import AD: Dual, xdual\n", + "pyplot()" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T01:07:43.203619", + "start_time": "2016-12-05T07:07:36.016Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "f (generic function with 1 method)" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "f(x,α,β,γ) = (α*(x)^2)/((((α-1.0)*(x^2))/β + γ + x))" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T01:07:43.311141", + "start_time": "2016-12-05T07:07:36.545Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "iteramapeo" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "\"\"\"\n", + "Este código nos permite iterar una función f n veces dada una condición inicial x0. \n", + "\"\"\"\n", + "function iteramapeo(f, x0, n)\n", + " xx = [x0]\n", + " fx = [0.0]\n", + " for it = 1:n\n", + " x1 = f(x0)\n", + " push!(xx, x0)\n", + " push!(fx, x1)\n", + " x0 = x1\n", + " push!(xx,x1)\n", + " push!(fx,x1)\n", + " end\n", + " xx, fx\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T01:07:43.313639", + "start_time": "2016-12-05T07:07:39.416Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(::#14) (generic function with 1 method)" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "#Aquí definimos el valor de los parámetros que utilizamos con la convención \\alpha \\equiv R, \\beta \\equiv M,\n", + "#\\gamma \\equiv S ```\n", + "α=500.0\n", + "β=10.0\n", + "γ=2.0\n", + "func = x -> f(x,α,β,γ)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T01:07:43.356637", + "start_time": "2016-12-05T07:07:40.663Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [], + "source": [ + "xfin,ffin = iteramapeo(func,200.0,10);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "Primero se realizó un análisis gráfico del mapeo" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T01:08:13.567663", + "start_time": "2016-12-05T07:08:13.073Z" + }, + "collapsed": false, + "scrolled": false, + "slideshow": { + "slide_type": "slide" + } + }, + "outputs": [ + { + "data": { + "text/html": [], + "text/plain": [ + "Interact.Slider{Float64}(Signal{Float64}(100.0, nactions=0),\"γ\",100.0,0.0:1.0:200.0,\".3f\",true)" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "" + ] + }, + "execution_count": 7, + "metadata": { + "comm_id": "b7486aaa-42c2-4cd0-9ac6-afd6bc76c0d3", + "reactive": true + }, + "output_type": "execute_result" + } + ], + "source": [ + "α = 10.0\n", + "β= 20.0\n", + "#``` Este código genera una gráfica interactiva del mapeo variando el parámetro \\gamma.\n", + "#```\n", + "@manipulate for γ in 0:1.0:200\n", + " pobla(x)=f(x,α,β,γ)\n", + " xfin,ffin = iteramapeo(pobla,10.0,16); #Añade la condición inicial con la que se analiza el mapeo y \n", + " #su trayectoria, la función definida un renglón arriba y el número de iteraciones.\n", + " plot(-10:1/32:100, pobla, xaxis=(L\"x\", (-10.0, 100.0)), yaxis=(L\"F_\\alpha(x)\",(-10.0,20.0))) # Hace la gráfica\n", + " #con especificaciones para ejees.\n", + " title!(\"Analisis grafico para distintos valores de S\")\n", + " plot!(-10:1/32:50, identity) #Grafica la identidad del análisis gráfico\n", + " plot!(xfin, ffin, marker=(:dot, 3, 0.4)) #Señala dónde terminó la condición inicial dada\n", + "end" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T00:06:39.575149", + "start_time": "2016-12-05T06:06:39.567Z" + }, + "collapsed": true, + "slideshow": { + "slide_type": "skip" + } + }, + "source": [ + "![Variando S](Figures/g1.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "Aquí mostramos una gráfica del comportamiento temporal del mapeo cuando $S=0$ y se varía la condición inicial." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T01:08:17.284291", + "start_time": "2016-12-05T07:08:17.279Z" + }, + "collapsed": false, + "scrolled": true, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "g (generic function with 1 method)" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "α = 10.0\n", + "β= 25.0\n", + "g(x,α,β)=(α*(x)^2)/((((α-1.0)*(x^2))/β + x)) #Define el mapeo con \\gamma = 0" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T01:08:18.195736", + "start_time": "2016-12-05T07:08:17.710Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "slide" + } + }, + "outputs": [ + { + "data": { + "text/html": [], + "text/plain": [ + "Interact.Slider{Float64}(Signal{Float64}(50.0, nactions=0),\"i\",50.0,0.0:1.0:100.0,\".3f\",true)" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "" + ] + }, + "execution_count": 9, + "metadata": { + "comm_id": "4a0bb2d9-308d-485b-8e83-890a59227dde", + "reactive": true + }, + "output_type": "execute_result" + } + ], + "source": [ + "@manipulate for i in 0:1.0:100 #Este código realiza una gráfica interactiva que cambia la condición inicial\n", + " # en cada paso entre 0 y 100 con los valores de \\alpha y \\beta dados anteriormente.\n", + " poblaciones(i) = g(i,α,β)\n", + " xfin,ffin = iteramapeo(poblaciones,i,20);\n", + " plot(0:1/32:100, poblaciones, xaxis=(L\"x\", (-10.0,100.0)), yaxis=(L\"F_\\alpha(x)\",(-100.0,100.0)))\n", + " title!(\"Evolucion de la poblacion sin insectos infertiles\")\n", + " plot!(0:1/32:100, identity)\n", + " plot!(xfin, ffin, marker=(:dot, 3, 0.4))\n", + "end" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "Vemos que en este caso, la población total nunca muere, tal como se esperaba, pues no hay insectos infértiles." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": false, + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "Se resolvió la ecuación $N(x)-x=0$ para encontrar los puntos fijos del mapeo en términos de los parámetros R,S y M, obteniendo:\n", + "\n", + "$X_{0}= 0$\n", + "\n", + "\n", + "y \n", + "\n", + "\n", + "\n", + "$X_{12}= \\frac{\\pm M(1-R)+\\sqrt{R-1}\\sqrt{M^{2}(1-R)-4MS}}{2(1-R)}$\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "Por lo que, para encontrar poblaciones estacionarias distintas de cero, tenemos que se deben cumplir las siguientes condiciones:\n", + "\n", + "$R> 1 $ ^ $M > \\frac{4S}{R-1}$" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T01:08:21.762009", + "start_time": "2016-12-05T07:08:21.650Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "INFO: Recompiling stale cache file /home/pablorv/.julia/lib/v0.5/NaNMath.ji for module NaNMath.\n", + "INFO: Recompiling stale cache file /home/pablorv/.julia/lib/v0.5/Roots.ji for module Roots.\n" + ] + } + ], + "source": [ + "using Roots" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T01:08:24.597799", + "start_time": "2016-12-05T07:08:24.587Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "puntofijo (generic function with 1 method)" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "function puntofijo(F::Function, range) #Este código calcula los puntos fijos de una función F en un rango range.\n", + " pf= fzeros(x -> (F(x) - x) , range)\n", + " return pf\n", + "end " + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T01:08:27.548054", + "start_time": "2016-12-05T07:08:27.536Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "F (generic function with 1 method)" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "α= 10.0\n", + "β= 25.0\n", + "γ= 50.0\n", + "\n", + "F(x) = (α*(x)^2)/((((α-1.0)*(x^2))/β + γ + x)) #Se define la función con nuevos parámetros arbitrarios, pero que\n", + "#cumplen las condiciones mencionadas." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T01:08:37.583836", + "start_time": "2016-12-05T07:08:28.182Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "3-element Array{Float64,1}:\n", + " 0.0 \n", + " 8.33333\n", + " 16.6667 " + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pf=puntofijo(F,[0,20.0]) #Se calculan los puntos fijos de éste mapeo." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T01:08:37.589452", + "start_time": "2016-12-05T07:08:31.416Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "g (generic function with 2 methods)" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "g(x)= (α*(x)^2)/((((α-1.0)*(x^2))/β + γ + x)) -x #Se define el mapeo que nos permite estudiar la localización \n", + "#de los puntos fijos al variar los parámetros." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T01:08:37.594141", + "start_time": "2016-12-05T07:08:32.254Z" + }, + "collapsed": false, + "scrolled": true, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(::#27) (generic function with 1 method)" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "α= 10.0\n", + "β= 25.0\n", + "γ= 50.0\n", + "func=x -> g(x) #Se dan valores a los parámetros para realizar un ejemplo de sus puntos fijos." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "A continuación se muestra una gráfica de los puntos fijos del mapeo en términos de los parámetros\n", + "$R=10$,$M=25$ y $S=50$." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T01:08:39.441692", + "start_time": "2016-12-05T07:08:34.711Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "slide" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plot(-10:1/32:30, func,xticks=-10:0.5:100,yticks=-10:0.5:50) #Se grafica el mapeo N(X)-x\n", + "xlabel!(L\"x\")\n", + "ylabel!(L\"N(x)-x\")\n", + "title!(\"Puntos fijos de N(x)\")\n", + "plot!([8.3,8.3], [1, -1, 0]) #Se marcan los puntos fijos sobre la gráfica.\n", + "plot!([0,0], [1, -1,0])\n", + "plot!([16.66, 16.66], [1, -1, 0])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "A continuación se muestran graficas que relacionan los parámetros y el comportamiento de los puntos fijos dependiendo de éstos." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "La función a estudiar es:\n", + "\n", + "$N(X)-X= \\frac{MRX^{2}}{(R-1)X^{2}+M(X+S)} -X $\n", + "\n", + " Nos interesa analizar este mapeo pues nos permite observar el comportamiento de los puntos fijos en función de los parámetros.\n", + " \n", + " En primer lugar, estudiemos a los puntos fijos para distintas $M$ en cada gráfica en función de $R$ y $S$ para una condición inicial fija $X_{0}=10.0$. " + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "PyPlot.Figure(PyObject )" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "INFO: Saved animation to /home/juser/tmp.gif\n" + ] + }, + { + "data": { + "text/html": [ + "\" />" + ], + "text/plain": [ + "Plots.AnimatedGif(\"/home/juser/tmp.gif\")" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pyplot(leg=false, ticks=nothing) #Este código realiza una gráfica para cada valor de M entre 1 y 80\n", + "x = y = linspace(2.0, 40, 40) #Establece el paso entre cada x,y y sus valores máximo y mínimo.\n", + "zs = zeros(0,40)\n", + "x0= 10.0 #Condición inicial arbitraria\n", + "@gif for i in linspace(1, 80, 100) #Creando el .gif, con 100 imágenes.\n", + " G(x,y) = (x*(x0)^2)/((((x-1.0)*(x0^2))/i + y + x0))-x0\n", + "\n", + "\n", + "plot(x, y, G, st = [:surface, :contourf],xaxis=(L\"R\",(-1.0, 50)),yaxis=(L\"S\",(-1.0, 50)),title=\"Puntos fijos del mapeo para distintas M\")\n", + " \n", + " end" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "![Distintas M](Figures/M.gif)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "Ahora estudiamos el comportamiento de los puntos fijos con un valor distinto de $R$ en cada gráfica que varía en función de $M$ y $S$." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "collapsed": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "PyPlot.Figure(PyObject )" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "INFO: Saved animation to /home/juser/tmp.gif\n" + ] + }, + { + "data": { + "text/html": [ + "\" />" + ], + "text/plain": [ + "Plots.AnimatedGif(\"/home/juser/tmp.gif\")" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pyplot(leg=false, ticks=nothing) #Este código realiza una gráfica para cada valor de R entre 1 y 100.\n", + "x = y = linspace(2.0, 40, 40)\n", + "zs = zeros(0,40)\n", + "x0= 10.0\n", + "@gif for i in linspace(1,100,100) #Se genera el .gif con 100 imágenes. \n", + " G(x,y) = (i*(x0)^2)/((((i-1.0)*(x0^2))/x + y + x0))-x0\n", + " title!(L\"Puntos fijos del mapeo\")\n", + " p = plot(x, y, G, st = [:surface, :contourf],xaxis=(L\"M\",(-1.0, 50)),yaxis=(L\"S\",(-1.0, 50)),title=\"Puntos fijos del mapeo para distintas R\")\n", + " \n", + " end" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true, + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "![Distintas R](Figures/R.gif)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "Finalmente, observemos la evolución de los puntos fijos para un valor distinto de $S$ en cada gráfica que se encuentra en\n", + "función de $M$ y $R$." + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "PyPlot.Figure(PyObject )" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "INFO: Saved animation to /home/juser/tmp.gif\n" + ] + }, + { + "data": { + "text/html": [ + "\" />" + ], + "text/plain": [ + "Plots.AnimatedGif(\"/home/juser/tmp.gif\")" + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "pyplot(leg=false, ticks=nothing) #Este código genera una gŕafica para cada valor de S en función de M y R.\n", + "x = y = linspace(2.0, 80, 90)\n", + "zs = zeros(0,90)\n", + "x0= 50.0 #Se utiliza otra condición inicial.\n", + "@gif for i in linspace(1, 100, 100) #Se construye el .gif con 100 imágenes también.\n", + " G(x,y) = (y*(x0)^2)/((((y-1.0)*(x0^2))/x + i + x0))-x0\n", + " title!(L\"Puntos fijos del mapeo\")\n", + " p = plot(x, y, G, st = [:surface, :contourf],xaxis=(L\"M\",(-1.0,100)),yaxis=(L\"R\",(-1.0, 100)),title=\"Puntos fijos del mapeo para distintas S\")\n", + " \n", + "end" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true, + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "![Distintas S](Figures/S.gif)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Bifurcaciones\n", + "\n", + "Una vez observado el comportamiento del mapeo en función de sus parámetros se prosiguió a encontrar para varios parámetros $R$ y $M$ el valor de $S$ para el cual la población desaparece" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T01:08:51.372051", + "start_time": "2016-12-05T07:08:51.360Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "diagbifurc" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "\"\"\"\n", + " ciclosestables!(xx, f, nit, nout, cc)\n", + "\n", + "Esta función itera el mapeo `f`, de una variable, `nit+nout` veces, \n", + "usando como condición inicial `x0=0`; los últimos `nout` iterados \n", + "actualizan al vector `xx` que tiene longitud `nout`. `cc` es el valor\n", + "del parámetro del mapeo `f`. El mapeo `f` debe ser definido de \n", + "tal manera que `f(x0,cc)` tenga sentido. La idea es los últimos \n", + "`nout` iterados reflejen los ciclos estables del mapeo `f`. \n", + "\"\"\"\n", + "function ciclosestables!(xx, f, nit, nout, cc,x0)\n", + " @assert nit > 0 && nout > 0\n", + " \n", + " # Primeros nit iterados\n", + " \n", + " for it = 1:nit\n", + " x0 = f(x0, cc)\n", + " end\n", + " \n", + " # Se guardan los siguientes nout iterados\n", + " for it = 1:nout\n", + " x0 = f(x0, cc)\n", + " @inbounds xx[it] = x0\n", + " end\n", + " \n", + " nothing\n", + "end\n", + "\n", + "\"\"\"\n", + " diagbifurc(f, nit, nout, crange)\n", + "\n", + "Itera el mapeo `f` `nit+nout` veces y regresa una matriz\n", + "cuya columna `i` tiene los últimos `nout` iterados del mapeo\n", + "para el valor del parámetro del mapeo `crange[i]`.\n", + "\n", + "La función `f` debe ser definida de tal manera que `f(x0, c)` \n", + "tenga sentido.\n", + "\"\"\"\n", + "function diagbifurc(f, nit, nout, crange,x0)\n", + " xx = Vector{Float64}(nout)\n", + " ff = Array{Float64,2}(nout, length(crange))\n", + " \n", + " for ic in eachindex(crange)\n", + " c = crange[ic]\n", + " ciclosestables!(xx, f, nit, nout, c,x0)\n", + " ff[:,ic] = xx\n", + " end\n", + " \n", + " return ff\n", + "end\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T01:08:54.970074", + "start_time": "2016-12-05T07:08:52.718Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [ + { + "ename": "LoadError", + "evalue": "LoadError: UndefVarError: scatter not defined\nwhile loading In[4], in expression starting on line 16", + "output_type": "error", + "traceback": [ + "LoadError: UndefVarError: scatter not defined\nwhile loading In[4], in expression starting on line 16", + "" + ] + } + ], + "source": [ + "Ict(x,m, r,s) = (r*x^2)/((r-1)*x^2/m + x + s)\n", + "\n", + "M=63\n", + "R=20\n", + "Ict1(x,s) = Ict(x,M,R,s)\n", + "\n", + "crange = 0:1000\n", + "\n", + "ff = diagbifurc(Ict1, 1000, 256, crange,50); \n", + "cc = ones(size(ff)[1])*crange';\n", + "\n", + "# Esto cambia las matrices en vectores; ayuda un poco para los dibujos\n", + "ff = reshape(ff, size(ff)[1]*size(ff)[2]);\n", + "cc = reshape(cc, size(ff));\n", + "\n", + "scatter(cc, ff, markersize= 0.05)\n", + "xlabel!(L\"S\")\n", + "ylabel!(L\"N\")\n", + "title!(\"Mapeo de SIT con M= 63 , R=20\")" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T01:08:55.595287", + "start_time": "2016-12-05T07:08:55.581Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "mapins (generic function with 1 method)" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "function intermap(M, R)\n", + " m1(x, s) = mapins(x, M, s, R)\n", + " srange = 0:2500.0\n", + " #map1 = mapeo_liap_all(srange, m1, 1000.0)\n", + " ff = diagbifurc(m1, 300, 10, srange, 1000); \n", + " cc = ones(size(ff)[1])*srange';\n", + "\n", + "# Esto cambia las matrices en vectores; ayuda un poco para los dibujos\n", + " ff = reshape(ff, size(ff)[1]*size(ff)[2]);\n", + " cc = reshape(cc, size(ff));\n", + " return ff, cc\n", + "end\n", + "#Mapeo\n", + "mapins(x, M, S, R) = (R*x^2)/((R - 1)*(x^2)/M + S + x)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T01:08:59.520160", + "start_time": "2016-12-05T07:08:57.758Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "slide" + } + }, + "outputs": [ + { + "data": { + "text/html": [], + "text/plain": [ + "Interact.Slider{Int64}(Signal{Int64}(50, nactions=0),\"M\",50,1:100,\"d\",true)" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [], + "text/plain": [ + "Interact.Slider{Float64}(Signal{Float64}(50.5, nactions=0),\"R\",50.5,1.1:0.1:100.0,\".3f\",true)" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "" + ] + }, + "execution_count": 20, + "metadata": { + "comm_id": "ebf7a472-b6b0-43ff-aa5f-ffa8581f91dc", + "reactive": true + }, + "output_type": "execute_result" + } + ], + "source": [ + "@manipulate for M in 1:100, R in 1.1:0.1:100\n", + " ff, cc = intermap(M, R)\n", + " scatter(cc, ff, markersize= 0.5, legend = :false, title =\"Diagrama de bifurcacion\", xlabel =L\"s\", ylabel =L\"x_{300}\")\n", + " xlims!(0, 2500)\n", + " ylims!(0, 100)\n", + "end" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "También hacemos el análisis del exponenete de Lyapunov" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T01:09:02.343432", + "start_time": "2016-12-05T07:09:02.223Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "mapeo_liap_all" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "doc\"\"\"\n", + " iterado(F,x0,n)\n", + "\n", + "Dado un punto $x_0$, esta funció guarda a todas la iteraciones bajo $F$ en un arreglo.\n", + "\"\"\"\n", + "\n", + "function iterado(F::Function,x0::Float64,n::Int)\n", + " y = Float64[x0] ##El primer elemento es x_0\n", + " x = x0\n", + " for i in 1:n\n", + " x=F(x) #El valor de x cambia con cada iteración\n", + " push!(y,x) #Este nuevo valor se guarda en el arreglo\n", + " end\n", + " y\n", + "end\n", + "\n", + "doc\"\"\"\n", + " Lyapunov(y, F)\n", + "\n", + "Dado un punto un arreglo que contenga todas las iteraciones bajo $F$ de $x_0$, calcula \n", + "$\\frac{1}{n} \\sum_{i=1}^n \\log\\Big| \\, f'(x_i)\\, \\Big|.$\n", + "\"\"\"\n", + "\n", + "function Lyapunov(y, F::Function)\n", + " n = length(y)\n", + " l = 0\n", + " \n", + " for i in 1:n\n", + " x = abs((F(xdual(y[i]))).der)\n", + " l = l + log(x)\n", + " \n", + " end\n", + " l/n\n", + "end\n", + "\n", + "doc\"\"\"\n", + "mapeo_liap_all(crange::FloatRange, Qc::Function, x0::Float64, n = 100000)\n", + "\n", + "Calcula el exponente de Lyapunov para un mapeo paramétrico $Q_c = Q_c(x, c)$ en un rango de parámetros `crange`, un\n", + "valor inicial `x0` y `n` iteraciones.\n", + "\"\"\"\n", + "\n", + "function mapeo_liap_all(crange::FloatRange, Qc::Function, x0::Float64, n = 100000)\n", + " mapeo = Float64[]\n", + " \n", + " for i in crange\n", + " Qci(x) = Qc(x,i) \n", + " y = iterado(Qci,x0,n)\n", + " l = Lyapunov(y, Qci)\n", + " if abs(l)\n", + "\n", + "Vemos cómo el rompimiento es un punto de bifurcación ya que $\\lambda = 0$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "Por último, se encontró a $S_c$ como función de $M$ y $R$, para esto empleamos el dominio $M\\times R = [1,100]\\times[1.1,100]$" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T01:09:08.994760", + "start_time": "2016-12-05T07:09:08.975Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "iteram (generic function with 1 method)" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "function iteram(M1::Range, R1::Range)\n", + " P, Q = length(R1), length(M1)\n", + " Mat1 = zeros(P, Q) \n", + " K = Int(P*Q)\n", + " n = 1\n", + " #@show (P, Q)\n", + " for j in 1:Q\n", + " for i in 1:P\n", + " if mod(100n/K, 5) == 0\n", + " println(100n/K, \"%\")\n", + " end\n", + " #@show i, j\n", + " M, R = M1[j], R1[i]\n", + " m1(x, s) = mapins(x, M, s, R)\n", + " srange = 0:3_000.0\n", + " #map1 = mapeo_liap_all(srange, m1, 1000.0)\n", + " ff = diagbifurc(m1, 300, 50, srange, 1000); \n", + " cc = ones(size(ff)[1])*srange';\n", + " \n", + " # Esto cambia las matrices en vectores; ayuda un poco para los dibujos\n", + " ff = reshape(ff, size(ff)[1]*size(ff)[2]);\n", + " cc = reshape(cc, size(ff));\n", + " for l in eachindex(ff)\n", + " if ff[l] == 0\n", + " Mat1[i, j] = cc[l]\n", + " break\n", + " end\n", + " end\n", + " n += 1\n", + " end\n", + " end\n", + "\n", + " mm = ones(size(Mat1)[1])*M1'\n", + " rr = R1*ones(size(Mat1)[2])'\n", + " A1 = reshape(Mat1, size(Mat1)[1]*size(Mat1)[2])\n", + " mm1 = reshape(mm, size(A1)[1])\n", + " rr1 = reshape(rr, size(A1)[1])\n", + " return mm1, rr1, A1\n", + "end" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "Con esto hemos hecho un mapeo preliminar con $M=1:50$ , $R=1:40$. Vemos el siguente comportamiento para \"cortes\" a R constante" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [], + "source": [ + "MS = readcsv(\"M1.csv\")\n", + "Rrange = 5:40;" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "collapsed": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [], + "source": [ + "plot(MS[1:10,1:5])\n", + "xlabel!(L\"M\")\n", + "ylabel!(L\"N\")\n", + "title!(\"Cortes a R=cte\");" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [], + "source": [ + "scatter(MS[1,:])\n", + "scatter!(MS[2,:])\n", + "scatter!(MS[3,:])\n", + "scatter!(MS[4,:])\n", + "xlabel!(L\"R\")\n", + "ylabel!(L\"N\")\n", + "title!(\"Cortes a M=cte\");" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "\n", + "\n", + "Vemos un comportamiento de agrupación en 4. Para indagar más en esto buscamos los puntos donde hay una crecimiento constante de $S_c$" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "([5.0,9.0,13.0,17.0,21.0,25.0,29.0,33.0,37.0],[1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0,9.0])" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "\n", + "dif=MS\n", + " for j in 1:length(MS[:,1])-1 #fixed r\n", + " dif[j,:]= MS[j+1,:]-MS[j,:]\n", + "end\n", + "\n", + "dif\n", + "dif[end,:]= dif[end-1,:]\n", + "steadyR = Float64[]\n", + "steapR = Float64[]\n", + "for i in 1:36\n", + " u = unique(dif[:,i])\n", + " if length(u)==1\n", + " push!(steadyR,Rrange[i])\n", + " push!(steapR,u[1])\n", + " end\n", + "end\n", + "steadyR,steapR" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(Float64[],Float64[])" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "MS = readcsv(\"M1.csv\")\n", + "Rrange = 5:40;\n", + "dif2=MS\n", + " for j in 1:length(MS[1,:])-1 #fixed m\n", + " dif2[:,j]= MS[:,j+1]-MS[:,j]\n", + "end\n", + "\n", + "dif2\n", + "dif[:,end]= dif[:,end-1]\n", + "steadyM = Float64[]\n", + "steapM = Float64[]\n", + "for i in 1:50\n", + " u = unique(dif[i,:])\n", + " if length(unique(dif[i,:]))==1\n", + " push!(steadyM,i)\n", + " push!(steapM,u[1])\n", + " end\n", + "end\n", + "steadyM,steapM" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T01:09:26.297429", + "start_time": "2016-12-05T07:09:24.044Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [], + "source": [ + "mm = readcsv(\"DatosPlano/mms2.csv\")[:,1]\n", + "rr = readcsv(\"DatosPlano/rrs2.csv\")[:,1]\n", + "cs = readcsv(\"DatosPlano/ccs2.csv\")[:,1];\n", + "append!(mm, readcsv(\"DatosPlano/mms3.csv\")[:,1])\n", + "append!(rr, readcsv(\"DatosPlano/rrs3.csv\")[:,1])\n", + "append!(cs, readcsv(\"DatosPlano/ccs3.csv\")[:,1]);\n", + "append!(mm, readcsv(\"DatosPlano/mms1.csv\")[:,1])\n", + "append!(rr, readcsv(\"DatosPlano/rrs1.csv\")[:,1])\n", + "append!(cs, readcsv(\"DatosPlano/ccs1.csv\")[:,1]);" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T01:10:02.663726", + "start_time": "2016-12-05T07:09:27.863Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "slide" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plot(mm, rr, cs, st = :surface)\n", + "xlabel!(\"M\")\n", + "ylabel!(\"R\")" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T01:10:18.451492", + "start_time": "2016-12-05T07:10:14.007Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + " \n", + "

Plotly javascript loaded.

\n", + "

To load again call

init_notebook(true)

\n", + " " + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "Plots.PlotlyJSBackend()" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "using Plots\n", + "plotlyjs()" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T01:10:22.463525", + "start_time": "2016-12-05T07:10:20.647Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [], + "source": [ + "mm = readcsv(\"DatosPlano/mms2.csv\")[:,1]\n", + "rr = readcsv(\"DatosPlano/rrs2.csv\")[:,1]\n", + "cs = readcsv(\"DatosPlano/ccs2.csv\")[:,1];\n", + "append!(mm, readcsv(\"DatosPlano/mms3.csv\")[:,1])\n", + "append!(rr, readcsv(\"DatosPlano/rrs3.csv\")[:,1])\n", + "append!(cs, readcsv(\"DatosPlano/ccs3.csv\")[:,1]);\n", + "append!(mm, readcsv(\"DatosPlano/mms1.csv\")[:,1])\n", + "append!(rr, readcsv(\"DatosPlano/rrs1.csv\")[:,1])\n", + "append!(cs, readcsv(\"DatosPlano/ccs1.csv\")[:,1]);" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "ExecuteTime": { + "end_time": "2016-12-05T01:10:35.775895", + "start_time": "2016-12-05T07:10:21.261Z" + }, + "collapsed": false, + "slideshow": { + "slide_type": "slide" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "\n", + " \n", + "\n", + "\n", + "
\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plot(mm, rr, cs)\n", + "xlabel!(\"M\")\n", + "ylabel!(\"R\")" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "# ¡Gracias por su atención!\n", + "\n", + "![](Figures/git.png)" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "celltoolbar": "Slideshow", + "kernelspec": { + "display_name": "Julia 0.5.0", + "language": "julia", + "name": "julia-0.5" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "0.5.0" + }, + "latex_envs": { + "bibliofile": "biblio.bib", + "cite_by": "apalike", + "current_citInitial": 1, + "eqLabelWithNumbers": true, + "eqNumInitial": 0 + } + }, + "nbformat": 4, + "nbformat_minor": 1 +}