Branch switching

• Branch switching
• • Branch switching from a Bogdanov–Takens (BT) point to a homoclinic curve

Branch switching from a Bogdanov–Takens (BT) point to a homoclinic curve

We provide an automatic branch switching method in this case (see for example the tutorial Autonomous electronic circuit (aBS from BT)). Hence, you can perform automatic branch switching by calling continuation with the following arguments:

continuation(prob_vf,
	bt,    # Bogdanov–Takens point
	bvp,   # discretization, e.g. Collocation or Shooting
	alg,   # continuation algorithm, e.g. PALC
	_contParams;
	ϵ0 = 1e-5, amplitude = 1e-3,
	maxT = Inf,
	kwargs...)

where prob_vf is the BifurcationProblem encoding the vector field and bt the Bogdanov–Takens point detected during a Fold or Hopf continuation, e.g. bt = get_normal_form(br, ind_bt). More information is available in the docstring of continuation and in the tutorials.