The natural way to start a Period Doubling bifurcation curve continuation is to start it from a Period Doubling bifurcation point on a limit cycle curve. This can be done using the following command: [x0,v0]=init_PD_PD(@odefile, x, s, ap, ntst, ncol). x should be the x as returned by the previous limit cycle continuation. s is the special point structure of the detected Period Doubling point on the limit cycle curve. odefile specifies the ode-file to be used. ap is the active parameter and ntst and ncol are again the number of mesh and collocation points for the discretization.
MATCONT provides four other initializers to start the continuation of PD curves from a codim2 bifurcation of limit cycles, namely init_GPD_PD.m, init_LPPD_PD.m, init_PDNS_PD.m and init_R2_PD.m.
These initializers are added for ease of use; they only refer back to init_PD_PD.m.
We note that MATCONT also provides an initializer init_PD_PD2.m which is merely an alternative to init_PD_PD.m; it is not to be confused
with the initializer init_PD_LC.m which initializes the computation of the period doubled curve from a PD point.