ON STOCHASTIC PERTURBATIONS OF DYNAMICAL SYSTEMS WITH FAST AND SLOW COMPONENTS

Dynamical systems with fast and slow components are considered. We show that small random perturbations of the fast component can lead to essential changes in the limiting slow motion. For example, new stable equilibria or deterministic oscillations with amplitude and frequency of order 1 can be introduced by the perturbations. These are stochastic resonance type effects, and they are considered from the point of view of large deviations theory.