MELNIKOV PROCESS FOR STOCHASTICALLY PERTURBED, SLOWLY VARYING OSCILLATORS - APPLICATION TO A MODEL OF WIND-DRIVEN COASTAL CURRENTS

The stochastic Melnikov approach is extended to a class of slowly vary ing dynamical systems. It is found that (1) necessary conditions for c haos induced by stochastic perturbations depend on the excitation spec trum and the transfer function in the expression for the Melnikov tran sform; (2) the Melnikov approach allows the estimation of lower bounds for (a) the mean time of exit from preferred regions of phase space, and (b) the probability that exits from those regions cannot occur dur ing a specified time interval. For a system modeling wind-induced curr ents, the deterministic Melnikov approach would indicate that chaotic transport cannot occur for certain parameter ranges. However, the more realistic stochastic Melnikov approach shows that, for those same par ameter ranges, the necessary conditions for exits during a specified t ime interval are satisfied with probabilities that increase as the rim e interval increases.