Limit cycles in slow-fast codimension 3 saddle and elliptic bifurcations

Abstract

In this paper we study singular perturbation problems occuring in planar slow-fast systems. We distinguish between slow-fast elliptic and slow-fast saddle bifurcations of codimension 3. These bifurcations are singular limits of well-known codimension 3 bifurcations. In this paper we focus on the appearance of small-amplitude limit cycles, using tools from geometric singular perturbation theory, including blow-up.