SageMath Tools for Stability and Bifurcation for Discrete Dynamical Systems

This paper presents some interactive tools, created in the computer algebra system SageMath, dealing with the stability and bifurcation for one- and two-dimensional discrete systems. The tools, geometrically, give information about the types of bifurcations (if any) and possible effects caused by the parameters. Using these tools, one can also obtain the basins of attraction of the fixed and periodic points, and the stability regions in parameter space.

Keywords

  • Parameter curves
  • Tr-det plane
  • Basin of attraction
  • Stability region
  • Discrete dynamical systems
  • Sagemath
  • Interactive tools

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