Quasi-deterministic approximation, metastability and stochastic resonance

For a wide class of dynamical systems perturbed by a random noise, we descr ibe the deterministic component of the long-time evolution of the perturbed system. In particular, for any initial point and for a given timescale, th e metastable state can be defined. Stochastic resonance is the result of th e 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 w hich is close to a large amplitude oscillation with the same period or with a period proportional to the period of determinisitic perturbation. All th ese effects are manifestations of the laws of the large deviations for the perturbed system. (C) 2000 Elsevier Science B.V. All rights reserved.