Hopf initialization

The most natural way to start the continuation of a Hopf bifurcation curve is to start it from a Hopf point, typically found on an equilibrium curve. The continuation of Hopf points cannot simply be started by using the following command:
[x,v,s,h,f]=cont(@hopf, x0, v0, opt)
The Hopf curve file has to know Also an initial point x0 has to be known. All this information can be supplied using the following command:
[x0,v0]=init_H_H(@odefile, xnew, p, ap).

The input arguments odefile, xnew, p, ap are built exactly as in init_LP_LP. The output vector x0 consists of $x_{new}$ extended with the free parameters and paramter $k$ from (62).

MATCONT provides four other initializers which allow to continue a Hopf curve by starting from a codim 2 equilibrium point. These are init_BT_H.m, init_GH_H.m, init_HH_H.m and init_ZH_H.m These initializers are added merely for ease of use since they refer back to init_H_H.m. However, we note that two Hopf curves pass through a Hopf point. So it can be necessary to specify the tangent vector to the desired Hopf curve.