pynamicalsys: A Python toolkit for the analysis of dynamical systems

IF 5.6 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals Pub Date : 2025-10-08 DOI:10.1016/j.chaos.2025.117269

Matheus Rolim Sales , Leonardo Costa de Souza , Daniel Borin , Michele Mugnaine , José Danilo Szezech , Ricardo Luiz Viana , Iberê Luiz Caldas , Edson Denis Leonel , Chris G. Antonopoulos

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引用次数: 0

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

, a simple yet powerful open-source Python module for the analysis of nonlinear dynamical systems. In particular,

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. We demonstrate the capabilities of

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.

is freely available via the Python Package Index (PyPI) and is intended to support both research and teaching in nonlinear dynamics.

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一个用于分析动态系统的Python工具包

自从洛伦兹在简化天气模式方面的开创性工作以来，非线性动力系统的数值分析已成为物理学研究的主要课题之一。尽管如此，仍然需要易于访问、高效和易于使用的计算工具来研究这些系统。在本文中，我们介绍了一个简单而强大的开源Python模块，用于分析非线性动力系统。特别是，▪实现了轨道仿真、分岔图、李雅普诺夫指数和其他一些混沌指标、周期轨道检测及其流形、以及逃逸和盆地分析的工具。我们通过一系列例子展示了▪的能力，这些例子再现了文献中众所周知的结果，同时发展了数学分析。我们还提供了包含本文中使用的所有代码的Jupyter笔记本，包括性能基准测试。▪可通过Python包索引（PyPI）免费获得，旨在支持非线性动力学的研究和教学。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Chaos Solitons & Fractals 物理-数学跨学科应用

CiteScore

13.20

自引率

10.30%

发文量

1087

审稿时长

9 months

期刊介绍： Chaos, Solitons & Fractals strives to establish itself as a premier journal in the interdisciplinary realm of Nonlinear Science, Non-equilibrium, and Complex Phenomena. It welcomes submissions covering a broad spectrum of topics within this field, including dynamics, non-equilibrium processes in physics, chemistry, and geophysics, complex matter and networks, mathematical models, computational biology, applications to quantum and mesoscopic phenomena, fluctuations and random processes, self-organization, and social phenomena.