MELNIKOV PROCESSES AND NOISE-INDUCED EXITS FROM A WELL

For a wide class of near-integrable systems with additive or multiplic ative noise the mean zero upcrossing rate for the stochastic system's Melnikov process tau(u)(-1), provides an upper bound for the system's mean exit rate, tau(e)(-1). Comparisons between tau(u)(-1) and tau e(- 1) show that in the particular case of additive white noise this upper bound is weak. For systems excited by processes with tail-limited dis tributions, the stochastic Melnikov approach yields a simple criterion guaranteeing the nonoccurrence of chaos. This is illustrated for the case of excitation by square-wave, coin-toss dichotomous noise. Finall y, we briefly review applications of the stochastic Melnikov approach to a study of the behavior of wind-induced fluctuating currents over a corrugated ocean floor; -the snap-trough of buckled columns with cont inuous mass distribution and distributed random loading; and open-loop control of stochastically excited multistable systems.