Multiple--Attractor Bifurcations and Quasiperiodicity in Nonsmooth Systems
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.