Multistability means the coexistence of several final states (attractors) for a given set of parameters. The long-term behavior of such systems becomes more involved, because there exists a nontrivial relationship between these coexisting asymptotic states and their basins of attraction. Multistable behavior is found in a variety of systems in different disciplines of science, as e.g. semiconductor physics, chemistry, neuroscience, and laser physics. Due to their complexly interwoven basins of attraction, multistable systems are extremely sensitive to perturbations. Small noise in such systems yields a hopping process between all the (meta-) stable states. This attractor hopping is determined by the structure of the underlying chaotic saddles embedded in the basin boundaries.
Basins of attraction for a periodically kicked rotor.
Hopping dynamics for a periodically kicked rotor.