Chaotic behaviour in a singularly perturbed system

Abstract

The aim of this paper is to present a novel type of chaos observed in a four dimensional singularly perturbed system. The chaotic behavior is described both numerically and analytically. We show the existence of a new type of strange attractor reminiscent of a chaotic behavior for a fast-slow system. Related to this we demonstrate that there is an invariant attracting region overlapping the jump manifolds of the fast system. This canonical problem was identi¯ed to be a coupled problem of two Hopf bifurcations with the fast jump process. We derive a geometric model where we can rigorously show the existence of chaotic orbits.