Multiple attractor bifurcation in a piecewise-smooth map with quasiperiodicity

Abstract

It is known that border-collision bifurcations in piecewise-smooth maps can lead to situations where several attractors are created simultaneously in so-called "multiple attractor" or "multiple choice" bifurcations. Phenomena of this type have also been observed in various physical and technical systems. We have recently demonstrated that piecewise-smooth systems can exhibit a new type of border-collision bifurcations in which a stable invariant curve, associated with a quasiperiodic or a periodic orbit, arises from a fixed point. In this paper we consider a particular variant of the multiple attractor bifurcation in which a stable periodic cycle arises simultaneously with a closed invariant curve. We also show examples of simultaneously appearing stable periodic orbits and of the simultaneous generation of periodic and chaotic attractors.