Yr. Sivathanu et al., EXITS IN MULTISTABLE SYSTEMS EXCITED BY COIN-TOSS SQUARE-WAVE DICHOTOMOUS NOISE - A CHAOTIC DYNAMICS APPROACH, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 52(5), 1995, pp. 4669-4675
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.