Stochastic global bifurcation in perturbed Hamiltonian systems
This paper deals with two perturbed Hamiltonian systems in which chaos-like dynamics can be induced by stochastic perturbations. For ordinary differential equations arising from two different fields, the population of epidemic model and the single mode periodically modulated laser model, the authors show that both systems can be reduced to the same weakly perturbed Hamiltonian system and have similar bifurcation structure and manifold structure that includes bi-instability and partially formed heteroclinic connections. In the presence of a bi-stability, they discuss how noise can induce a global bifurcation and chaos-like dynamics which exhibits mixed mode behavior of the original bi-stable solutions, using numerical approximations to the transport between basins.
scientific article; zbMATH DE number 2046175