- Author
- Sivathanu, Y. R. | Hagwood, C. | Simiu, E.
- Title
- Exits in Multistable Systems Excited by Coin-Toss Square-Wave Dichotomous Noise: A Chaotic Dynamics Approach.
- Coporate
- Purdue Univ., West Lafayette, IN National Institute of Standards and Technology, Gaithersburg, MD
- Journal
- Physical Review E, Vol. 52, No. 5, 4669-4675, November 1995
- Sponsor
- Office of Naval Research, Washington, DC
- Contract
- ONR-GRANT-N00014-94-0028
- Keywords
- noise (sound) | exits | Melnikov process
- Identifiers
- dynamical systems; necessary condition for the occurrence of exits; Melnikov process and criterion guaranteeing the nonoccurrence of exits; mean exit time and probability of no exits during a specified time interval
- 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.