User guide

The user guide explains the ideas behind mappy-ds and how to use its parts together. If you have not done so yet, start with the tutorial.

• Concept of modes
  • Modes
  • Borders
  • Transitions
  • Initial and end modes
  • The mode graph
  • Mode history
  • Discrete-time systems
• Jacobian and Hessian tensor
  • Index conventions
  • Symbolic tracing of system functions
  • Discrete modes
  • Continuous modes
  • Parameter derivatives
  • Mixed derivatives
  • Composition
  • Accuracy
• Periodic points, bifurcations, continuation
  • Periodic points: find_cycle
  • Following a cycle: trace_cycle
  • Through folds: trace_cycle_arclength
  • Local bifurcations: find_local_bf
  • Bifurcation curves: trace_local_bf
  • Bifurcation curves through cusps: trace_local_bf_arclength
  • Reading ContinuationStep
  • Custom continuation
• Plotting
  • Trajectories
  • Static plots: plot_trajectory
  • Interactive plots: plot2d
• Working examples
  • Hénon map
  • Izhikevich neuron
  • Forced Duffing oscillator
  • Forced Alpazur oscillator
  • Three-dimensional coupled logistic map

Reference

Y. Miino, “Mode concept to construct diffeomorphisms representing smooth/non-smooth dynamical systems”, Nonlinear Theory and Its Applications, IEICE, vol. 15, no. 2, pp. 284–298, 2024. doi:10.1587/nolta.15.284