Multistability in dynamical systems
Abstract
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.
Cite
@article{arxiv.chao-dyn/9904004,
title = {Multistability in dynamical systems},
author = {R. Vilela Mendes},
journal= {arXiv preprint arXiv:chao-dyn/9904004},
year = {2007}
}
Comments
11 pages Latex, to appear in Dynamical Systems: From Crystal to Chaos, World Scientific, 1999