Quasi-deterministic approximation, metastability and stochastic resonance

For a wide class of dynamical systems perturbed by a random noise, we describe the deterministic component of the long-time evolution of the perturbed system. In particular, for any initial point and for a given timescale, the metastable state can be defined. Stochastic resonance is the result of the change of the metastable state if a relatively small and slowly changing deterministic perturbation is added to the system. If this perturbation is periodic, then under certain assumption, the system will perform a motion which is close to a large amplitude oscillation with the same period or with a period proportional to the period of determinisitic perturbation. All these effects are manifestations of the laws of the large deviations for the perturbed system.