Pynamical: Model and Visualize Discrete Nonlinear Dynamical Systems, Chaos, and Fractals

Journal of Open Source Education, 1(1), 15 (2018)

3 Pages Posted: 13 Jul 2018

See all articles by Geoff Boeing

Geoff Boeing

University of Southern California - Sol Price School of Public Policy

Date Written: June 21, 2018

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.

Keywords: chaos, fractal, nonlinearity, nonlinear systems, attractor, bifurcation, chaotic, dynamical, geometry, mathematics, modeling, simulation, physics, prediction, python, visualization, systems analysis

JEL Classification: C6

Suggested Citation

Boeing, Geoff, Pynamical: Model and Visualize Discrete Nonlinear Dynamical Systems, Chaos, and Fractals (June 21, 2018). Journal of Open Source Education, 1(1), 15 (2018). Available at SSRN: https://ssrn.com/abstract=3200699

Geoff Boeing (Contact Author)

University of Southern California - Sol Price School of Public Policy ( email )

Los Angeles, CA 90089-0626
United States

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