American Institute of Mathematical Sciences

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2003, 2003(Special): 123-132. doi: 10.3934/proc.2003.2003.123

Stochastic global bifurcation in perturbed Hamiltonian systems

Lora Billings 1, , Erik M. Bollt 2, , David Morgan 3, and  Ira B. Schwartz 3,

1. 

Department of Mathematical Sciences, Montclair State University, Upper Montclair, NJ 07043, United States
2. 

Clarkson University, P.O. Box 5815, Potsdam, NY 13699-5815, United States
3. 

Naval Research Laboratory, Code 6792, Plasma Physics Division, Washington, DC 20375, United States, United States

Received  August 2002 Revised  April 2003 Published  April 2003

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, chaos., bifurcation, Hamiltonian.
Mathematics Subject Classification: 34F05, 65P20, 34D08, 37M2.
Citation: Lora Billings, Erik M. Bollt, David Morgan, Ira B. Schwartz. Stochastic global bifurcation in perturbed Hamiltonian systems. Conference Publications, 2003, 2003 (Special) : 123-132. doi: 10.3934/proc.2003.2003.123
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