Multistability in dynamical systems
Abstract
Description
In neuroscience, optics and condensed matter there is ample physical evidence for multistable dynamical systems, that is, systems with a large number of attractors. The known mathematical mechanisms that lead to multiple attractors are homoclinic tangencies and stabilization, by small perturbations or by coupling, of systems possessing a large number of unstable invariant sets. A short review of the existent results is presented, as well as two new results concerning the existence of a large number of stable periodic orbits in a perturbed marginally stable dissipative map and an infinite number of such orbits in two coupled quadratic maps working on the Feigenbaum accumulation point.
11 pages Latex, to appear in Dynamical Systems: From Crystal to Chaos, World Scientific, 1999
11 pages Latex, to appear in Dynamical Systems: From Crystal to Chaos, World Scientific, 1999