Chaotic dynamics with Maxima

TL;DR

This paper introduces chaos theory concepts in dynamical systems using Maxima, a free cross-platform computer algebra system, covering topics like bifurcations, Lyapunov exponents, and strange attractors.

Contribution

It provides an accessible, software-based approach to studying chaos in dynamical systems using Maxima, emphasizing standard techniques and visualizations.

Findings

Demonstrates bifurcation diagrams and chaos transition

Calculates Lyapunov exponents and fractal dimensions

Uses Maxima for modeling Lorentz and Duffing systems

Abstract

We present an introduction to the study of chaos in discrete and continuous dynamical systems using the CAS Maxima. These notes are intended to cover the standard topics and techniques: discrete and continuous logistic equation to model growth population, staircase plots, bifurcation diagrams and chaos transition, nonlinear continuous dynamics (Lorentz system and Duffing oscillator), Lyapunov exponents, Poincar\'e sections, fractal dimension and strange attractors. The distinctive feature here is the use of free software with just one ingredient: the CAS Maxima. It is cross-platform and have extensive on-line documentation.