analysis.rst

brainpy.analysis module

.. currentmodule:: brainpy.analysis

.. automodule:: brainpy.analysis

Contents

• Summary
• Phase Plane Analysis
• Bifurcation Analysis
• Fast-slow System Analysis
• Useful Functions

Summary

.. autosummary::
    :toctree: _autosummary

    PhasePlane
    Bifurcation
    FastSlowBifurcation

    get_1d_stability_types
    get_2d_stability_types
    get_3d_stability_types
    stability_analysis

Phase Plane Analysis

We provide a fundamental class PhasePlane to help users make phase plane analysis for 1D/2D dynamical systems. Five methods are provided, which can help you to plot:

• Fixed points
• Nullcline (zero-growth isoclines)
• Vector filed
• Limit cycles
• Trajectory

.. autoclass:: PhasePlane
    :members: plot_fixed_point, plot_nullcline, plot_trajectory, plot_vector_field, plot_limit_cycle_by_sim

Bifurcation Analysis

We also provide basic bifurcation analysis for 1D/2D dynamical systems.

.. autoclass:: Bifurcation
    :members: plot_bifurcation, plot_limit_cycle_by_sim

Fast-slow System Analysis

For some 3D dynamical system, which can be treated as a fast-slow system, they can be easily analyzed through our provided FastSlowBifurcation.

.. autoclass:: FastSlowBifurcation
    :members: plot_bifurcation

Useful Functions

In brainpy.analysis module, we also provide several useful functions which may help your dynamical system analysis.

>>> get_1d_stability_types()
['saddle node', 'stable point', 'unstable point']

>>> get_2d_stability_types()
['saddle node',
 'center',
 'stable node',
 'stable focus',
 'stable star',
 'center manifold',
 'unstable node',
 'unstable focus',
 'unstable star',
 'unstable line',
 'stable degenerate',
 'unstable degenerate']