Modelling Chaos
Study and Simulation of Bifurcation Systems

Abstract

The purpose of this work is to present the reader with an introduction to linear chaotic systems. We conduct a study of deterministic chaos, proving that the one-dimensional map $f^{n+1}(x_n);=\mu x_n (1-x_n)$ meets the requirements for a chaotic system defined by Devaney. Further into the work we obtain Feigenbaums constant using 3 different methods, with the best value obtained being $\delta = 4.6692016$.

The data has been generated using independently written software. The software utilises techniques from multiprocessing in order to decrease data processing time, thus allowing for more computationally demanding tasks to be attempted.