EXITS IN MULTISTABLE SYSTEMS EXCITED BY COIN-TOSS SQUARE-WAVE DICHOTOMOUS NOISE - A CHAOTIC DYNAMICS APPROACH

We consider a wide class of multistable systems perturbed by a dissipa tive term and coin-toss square-wave dichotomous noise. These systems b ehave like their harmonically or quasiperiodically driven counterparts : depending upon the system parameters, the steady-state motion is cof ined to one well for all time or experiences exits from the wells. Thi s similarity suggests the application to the stochastic systems of a M elnikov approach originally developed for the deterministic case. The noise induces a Melnikov process that may be used to obtain a simple c ondition guaranteeing the nonoccurrence of exits from a well. For syst ems whose unperturbed counterparts have phase space dimension 2, if th at condition is not satisfied, weak lower bounds can be obtained for ( a) the mean time of exit from a well and (b) the probability that exit s will not occur during a specified time interval.