Fold of cycles initialization

One way to start a Fold bifurcation of cycles continuation supported in the current version is to start it from a fold bifurcation point (LPC) on a limit cycle curve. This can be done using the following command: [x0,v0]=init_LPC_LPC(@odefile, x, s, ap, ntst, ncol $(,bp)_{optional}$). x should be the x as returned by the previous limit cycle continuation. s is the special point structure of the detected Fold bifurcation 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. bp are the optional indices of the branch parameters. It also works without entering a value for this field: [x0,v0]=init_LPC_LPC(@odefile, x, s, ap, ntst, ncol).

MATCONT provides four other initializers which allow to start a continuation of folds of limit cycles by starting from an codim2 bifurcation of limit cycles. These are init_CPC_LPC.m, init_LPNS_LPC.m, init_LPPD_LPC.m and init_R1_LPC.m. These initializers are introduced for ease of use since they refer back to init_LPC_LPC.m.

A more interesting and indeed nontrivial initializer is init_GH_LPC.m. Computational methods to switch to nonhyperbolic cycles from codim 2 bifurcations of equilibria are discussed in [29].