Abstracts

Topic: Y. R. Sivathanu, C. Hagwood, and E. Simiu (1995),

“Exits in Multistable Systems Excited by Coin-toss Square-wave Dichotomous Noise: A Chaotic Dynamics Approach,”

Physical Review E, vol. 52, no. 5, pp. 4669-4675.

We consider a wide class of multistable systems perturbed by a dissipative term and coin-toss square-wave dichotomous noise. These systems behave like their harmonically or quasiperiodically driven counterparts: depending upon the system parameters, the steady-state motion is confined to one well for all time or experiences exits from the wells. This similarity suggests the application to the stochastic systems of a Melnikov approach originally developed for the deterministic case. The noise induces a Melnikov process that may be used to obtain a simple condition guaranteeing the nonoccurrence of exits from a well. For systems whose unperturbed counterparts have phase space dimension 2, if that 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 exits will not occur during a specified time interval.