Stochastic Global Bifurcation in Perturbed Hamiltonian Systems

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.