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Stochastic global bifurcation in perturbed Hamiltonian systems

Pages: 123 - 132, Issue Special, July 2003

 Abstract        Full Text (787.2K)              

Lora Billings - Department of Mathematical Sciences, Montclair State University, Upper Montclair, NJ 07043, United States (email)
Erik M. Bollt - Clarkson University, P.O. Box 5815, Potsdam, NY 13699-5815, United States (email)
David Morgan - Naval Research Laboratory, Code 6792, Plasma Physics Division, Washington, DC 20375, United States (email)
Ira B. Schwartz - Naval Research Laboratory, Code 6792, Plasma Physics Division, Washington, DC 20375, United States (email)

Abstract: We study two perturbed Hamiltonian systems in which chaos-like dynamics can be induced by stochastic perturbations. We show the similarities of a class of population and laser models, analytically and topologically. Both systems have similar manifold structure that includes bi-instability and partially formed heteroclinic connections. Noise takes advantage of this structure, inducing a global bifurcation and chaotic-like dynamics which exhibits mixed mode behavior of the original bi-stable solutions. We support these claims with numerical approximations of the transport between basins.

Keywords:  Stochastic dynamical systems, Hamiltonian, bifurcation, chaos.
Mathematics Subject Classification:  34F05, 65P20, 34D08, 37M20.

Received: August 2002;      Revised: April 2003;      Published: April 2003.