Multiple attractor bifurcations: A source of unpredictability in piecewisesmooth systems

There exists a variety of physically interesting situations described by co ntinuous maps that are nondifferentiable on some surface in phase space. Su ch systems exhibit novel types of bifurcations in which multiple coexisting attractors can be created simultaneously. The striking feature of these bi furcations is that in the presence of arbitrarily small noise they lead to fundamentally unpredictable behavior of orbits as a system parameter is var ied slowly through its bifurcation value. This unpredictability gradually d isappears as the speed of variation of the system parameter through the bif urcation is reduced to zero.