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Exits in Multistable Systems Excited by Coin-Toss Square-Wave Dichotomous Noise: A Chaotic Dynamics Approach.


pdf icon Exits in Multistable Systems Excited by Coin-Toss Square-Wave Dichotomous Noise: A Chaotic Dynamics Approach. (574 K)
Sivathanu, Y. R.; Hagwood, C.; Simiu, E.

Physical Review E, Vol. 52, No. 5, 4669-4675, November 1995.

Sponsor:

Office of Naval Research, Washington, DC

Keywords:

noise (sound); exits; Melnikov process

Abstract:

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.