Animated phase portraits of nonlinear and chaotic dynamical systems

TL;DR

This paper introduces programs that generate animated phase portraits of nonlinear and chaotic systems like Van der Pol, Chua, and Lorenz models, aiding in understanding their complex dynamics through visualizations.

Contribution

It presents new software tools for animated visualization of phase portraits in 2D and 3D for complex dynamical systems.

Findings

Enhanced understanding of system dynamics through visualization

Tools applicable to multiple nonlinear models

Facilitation of educational and research analysis

Abstract

The aim of this section is to present programs allowing to high- light the slow-fast evolution of the solutions of nonlinear and chaotic dynamical systems such as: Van der Pol, Chua and Lorenz models. These programs provide animated phase portraits in dimension two and three, i.e. integration step by step" which are useful tools enabling to understand the dynamic of such systems.