# Bifurcation2D#

class brainpy.analysis.Bifurcation2D(model, target_pars, target_vars, fixed_vars=None, pars_update=None, resolutions=None, options=None)[source]#

Bifurcation analysis of 2D system.

Using this class, we can make co-dimension1 or co-dimension2 bifurcation analysis.

plot_bifurcation(with_plot=True, show=False, with_return=False, tol_aux=1e-08, tol_unique=0.01, tol_opt_candidate=None, num_par_segments=1, num_fp_segment=1, nullcline_aux_filter=1.0, select_candidates='aux_rank', num_rank=100)[source]#

Make the bifurcation analysis.

Parameters:
• with_plot (bool) – Whether plot the bifurcation figure.

• show (bool) – Whether show the figure.

• with_return (bool) – Whether return the computed bifurcation results.

• tol_aux (float) – The loss tolerance of auxiliary function $$f_{aux}$$ to confirm the fixed point. Default is 1e-7. Once $$f_{aux}(x_1) < \mathrm{tol\_aux}$$, $$x_1$$ will be a fixed point.

• tol_unique (float) – The tolerance of distance between candidate fixed points to confirm they are the same. Default is 1e-2. If $$|x_1 - x_2| > \mathrm{tol\_unique}$$, then $$x_1$$ and $$x_2$$ are unique fixed points. Otherwise, $$x_1$$ and $$x_2$$ will be treated as a same fixed point.

• tol_opt_candidate (float, optional) – The tolerance of auxiliary function $$f_{aux}$$ to select candidate initial points for fixed point optimization.

• num_par_segments (int, sequence of int) – How to segment parameters.

• num_fp_segment (int) – How to segment fixed points.

• nullcline_aux_filter (float) – The

• select_candidates (str) –

The method to select candidate fixed points. It can be:

• fx-nullcline: use the points of fx-nullcline.

• fy-nullcline: use the points of fy-nullcline.

• nullclines: use the points in both of fx-nullcline and fy-nullcline.

• aux_rank: use the minimal value of points for the auxiliary function.

• num_rank (int) – The number of candidates to be used to optimize the fixed points. rank to use.

Returns:

results – Return a tuple of analyzed results:

• fixed points: a 2D matrix with the shape of (num_point, num_var)

• parameters: a 2D matrix with the shape of (num_point, num_par)

• jacobians: a 3D tensors with the shape of (num_point, 2, 2)

Return type:

tuple