Nonlinear System Dynamics

Nonlinear Dynamics Systems

1-Dimensional Systems

Logistic Map

Euler Method

Fixed Points Stability

Pitchfork Bifurcation

Neuron Model

Laser

Adler equation

Delayed Logistic equation

Stability Test

2-Dimensional Systems

2D System Phase Portrait

Direction Field

Chaotic Systems - Lorenz System

Let us consider the Lorenz system: $$ \begin{array}{r} \dot{x}=\sigma(y-x) \ \dot{y}=\rho x-y-x z \ \dot{z}=-\beta z+x y \end{array} $$

Maximum Lyapunov Exponent

Henon Map

Rossler System