pynamicalsys: A Python toolkit for the analysis of dynamical systems

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...

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Published in:Chaos, solitons and fractals Vol. 201; p. 117269
Main Authors: Sales, Matheus Rolim, de Souza, Leonardo Costa, Borin, Daniel, Mugnaine, Michele, Szezech, José Danilo, Viana, Ricardo Luiz, Caldas, Iberê Luiz, Leonel, Edson Denis, Antonopoulos, Chris G.
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.12.2025
Subjects:
Chaos theory
Nonlinear dynamical systems
Python package
Chaos theory
Python package
Nonlinear dynamical systems
ISSN:0960-0779
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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. •An open source Python package for the analysis of dynamical systems.•pynamicalsys includes bifurcation diagrams, chaotic indicators, periodic orbits detection and their manifolds.•The package also includes quantification of basins of attractions, such as basin entropy and boundary dimension.
AbstractList 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. •An open source Python package for the analysis of dynamical systems.•pynamicalsys includes bifurcation diagrams, chaotic indicators, periodic orbits detection and their manifolds.•The package also includes quantification of basins of attractions, such as basin entropy and boundary dimension.
ArticleNumber 117269
Author Borin, Daniel
Caldas, Iberê Luiz
Szezech, José Danilo
Viana, Ricardo Luiz
Leonel, Edson Denis
Antonopoulos, Chris G.
Sales, Matheus Rolim
Mugnaine, Michele
de Souza, Leonardo Costa
Author_xml – sequence: 1
  givenname: Matheus Rolim
  orcidid: 0000-0002-1121-6371
  surname: Sales
  fullname: Sales, Matheus Rolim
  email: rolim.sales.m@gmail.com
  organization: University of Essex, School of Mathematics, Statistics and Actuarial Science, Wivenhoe Park, Colchester, CO4 3SQ, United Kingdom
– sequence: 2
  givenname: Leonardo Costa
  orcidid: 0000-0002-1272-6891
  surname: de Souza
  fullname: de Souza, Leonardo Costa
  organization: Institute of Physics, University of São Paulo, 05315-970, São Paulo, SP, Brazil
– sequence: 3
  givenname: Daniel
  orcidid: 0000-0002-4098-7730
  surname: Borin
  fullname: Borin, Daniel
  organization: São Paulo State University (UNESP), Institute of Geosciences and Exact Sciences, 13506-900, Rio Claro, SP, Brazil
– sequence: 4
  givenname: Michele
  orcidid: 0000-0002-8169-4723
  surname: Mugnaine
  fullname: Mugnaine, Michele
  organization: Institute of Physics, University of São Paulo, 05315-970, São Paulo, SP, Brazil
– sequence: 5
  givenname: José Danilo
  orcidid: 0000-0001-8306-8315
  surname: Szezech
  fullname: Szezech, José Danilo
  organization: Institute of Physics, University of São Paulo, 05315-970, São Paulo, SP, Brazil
– sequence: 6
  givenname: Ricardo Luiz
  orcidid: 0000-0001-7298-9370
  surname: Viana
  fullname: Viana, Ricardo Luiz
  organization: Federal University of Paraná, Department of Physics, Interdisciplinary Center for Science, Technology and Innovation, Center for Modeling and Scientific Computing, 81531-980, Curitiba, PR, Brazil
– sequence: 7
  givenname: Iberê Luiz
  orcidid: 0000-0002-1748-0106
  surname: Caldas
  fullname: Caldas, Iberê Luiz
  organization: Institute of Physics, University of São Paulo, 05315-970, São Paulo, SP, Brazil
– sequence: 8
  givenname: Edson Denis
  orcidid: 0000-0001-8224-3329
  surname: Leonel
  fullname: Leonel, Edson Denis
  organization: São Paulo State University (UNESP), Institute of Geosciences and Exact Sciences, 13506-900, Rio Claro, SP, Brazil
– sequence: 9
  givenname: Chris G.
  orcidid: 0000-0001-7195-6892
  surname: Antonopoulos
  fullname: Antonopoulos, Chris G.
  email: canton@essex.ac.uk
  organization: University of Essex, School of Mathematics, Statistics and Actuarial Science, Wivenhoe Park, Colchester, CO4 3SQ, United Kingdom
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SSID ssj0001062
Score 2.4721186
Snippet 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...
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StartPage 117269
SubjectTerms Chaos theory
Nonlinear dynamical systems
Python package
Title pynamicalsys: A Python toolkit for the analysis of dynamical systems
URI https://dx.doi.org/10.1016/j.chaos.2025.117269
Volume 201
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