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Pynamical: Model and visualize discrete nonlinear dynamical systems, chaos, and fractals

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  • Boeing, Geoff

    (Northeastern University)

Abstract

Pynamical is an educational Python package for introducing the modeling, simulation, and visualization of discrete nonlinear dynamical systems and chaos, focusing on one-dimensional maps (such as the logistic map and the cubic map). Pynamical facilitates defining discrete one-dimensional nonlinear models as Python functions with just-in-time compilation for fast simulation. It comes packaged with the logistic map, the Singer map, and the cubic map predefined. The models may be run with a range of parameter values over a set of time steps, and the resulting numerical output is returned as a pandas DataFrame. Pynamical can then visualize this output in various ways, including with bifurcation diagrams, two-dimensional phase diagrams, three-dimensional phase diagrams, and cobweb plots. These visualizations enable simple qualitative assessments of system behavior including phase transitions, bifurcation points, attractors and limit cycles, basins of attraction, and fractals.

Suggested Citation

  • Boeing, Geoff, 2018. "Pynamical: Model and visualize discrete nonlinear dynamical systems, chaos, and fractals," SocArXiv g8nsf, Center for Open Science.
  • Handle: RePEc:osf:socarx:g8nsf
    DOI: 10.31219/osf.io/g8nsf
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    References listed on IDEAS

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    1. Boeing, Geoff, 2017. "Visual Analysis of Nonlinear Dynamical Systems: Chaos, Fractals, Self-Similarity and the Limits of Prediction," SocArXiv c7p43, Center for Open Science.
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