mappy_ds.root.trace_local_bf#

mappy_ds.root.trace_local_bf(diffeo, y0, params, bf_param_key, theta, cnt_param_key, end_value, *, period=1, resolution=100, show_progress=False, callback=None, **root_options)#

Continue a local bifurcation along a second parameter.

params[cnt_param_key] is swept from its current value to end_value; at each point find_local_bf() solves for the periodic point, params[bf_param_key] and theta, starting from the previous solution. The result traces a bifurcation curve in the (cnt_param_key, bf_param_key) plane.

Parameters:

diffeoMap: The map.
y0array_like: Initial guess of the periodic point, ideally at a bifurcation point found with find_local_bf().
paramsmapping: Initial parameters; not modified.
bf_param_keystr: Key of the bifurcation parameter (solved at each step).
thetafloat: Initial argument of the critical multiplier; see find_local_bf().
cnt_param_keystr: Key of the continued parameter.
end_valuefloat: Final value of params[cnt_param_key].
periodint, optional: Period of the cycle, by default 1.
resolutionint, optional: Number of continuation points including both ends, by default 100.
show_progressbool, optional: Print progress to standard error, by default False.
callbackcallable, optional: Called with each successful step (as returned in the list).
**root_options: Forwarded to scipy.optimize.root().

Returns:

list of ContinuationStep: One step per bifurcation point found. y is the periodic point, params holds both the continued and the solved bifurcation parameter, and info holds theta, eigvals, eigvecs, nfev and residual.

Raises:

ValueError: If bf_param_key equals cnt_param_key.