NEAR-RESONANT MOTIONS IN SYSTEMS WITH RANDOM PERTURBATIONS

The effect of random perturbations on near-resonant motions in non-lin ear oscillatory systems is investigated. It is assumed that the equati ons of motion of the system can be reduced to standard form with a sma ll parameter epsilon, and that an isolated primary resonance exists in the unperturbed system [1]. The behaviour of the perturbed system in the epsilon-neighbourhood of the resonance surface is considered and a n effect analogous to deterministic ''capture in resonance'' [1] in an asymptotically long time interval is investigated. (C) 1998 Elsevier Science Ltd. All rights reserved.