Multistability in dynamical systems

Details Multistability in dynamical systems Multistability in dynamical systems

1999-03-30

arxiv.org/abs/chao-dyn/9904004v1

Nonlinear Sciences

Chaotic Dynamics

11 pages Latex, to appear in Dynamical Systems: From Crystal to Chaos, World Scientific, 1999

Scientific paper

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.

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