pynamicalsys: A Python toolkit for the analysis of dynamical systems

TL;DR

pynamicalsys is an open-source Python toolkit that provides comprehensive tools for analyzing nonlinear dynamical systems, including simulation, bifurcation analysis, chaos indicators, and model customization, supporting research and education.

Contribution

It introduces a user-friendly, efficient Python module with extensive features for nonlinear dynamics analysis, including built-in models and easy custom model integration.

Findings

Successfully reproduces well-known dynamical systems results

Demonstrates efficient performance through benchmarks

Supports both research and teaching applications

Abstract

Since Lorenz's seminal work on a simplified weather model, the numerical analysis of nonlinear dynamical systems has become one of the main subjects of research in physics. Despite of that, there remains a need for accessible, efficient, and easy-to-use computational tools to study such systems. In this paper, we introduce pynamicalsys, a simple yet powerful open-source Python module for the analysis of nonlinear dynamical systems. In particular, pynamicalsys implements tools for trajectory simulation, bifurcation diagrams, Lyapunov exponents and several others chaotic indicators, period orbit detection and their manifolds, as well as escape and basins analysis. It also includes many built-in models and the use of custom models is straighforward. We demonstrate the capabilities of pynamicalsys through a series of examples that reproduces well-known results in the literature while developing the mathematical analysis at the same time. We also provide the Jupyter notebook containing all the code used in this paper, including performance benchmarks. pynamicalsys is freely available via the Python Package Index (PyPI) and is indented to support both research and teaching in nonlinear dynamics.