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Stochastic global bifurcation in perturbed Hamiltonian systems

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  • 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.
    Mathematics Subject Classification: 34F05, 65P20, 34D08, 37M20.

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