Saddle-node bifurcation of canard limit cycles in piecewise linear systems

Abstract

We study saddle-node bifurcations of canard limit cycles in PWL systems by using singular perturbation theory tools. We distinguish two cases: the subcritical and the supercritical. In the subcritical case, we find saddle-node bifurcations of canard cycles both with head and without head. Moreover, we detect a transition between them. In the supercritical case, we find situations with two saddle-node bifurcations, which take place exponentially close in the parameter space; one of headless canards and another of canards with head. There, three canard cycles can coexist.