Exits in Multistable Systems Excited by Coin-Toss Square-Wave Dichotomous Noise: A Chaotic Dynamics Approach.
Exits in Multistable Systems Excited by Coin-Toss
Square-Wave Dichotomous Noise: A Chaotic Dynamics
Sivathanu, Y. R.; Hagwood, C.; Simiu, E.
Physical Review E, Vol. 52, No. 5, 4669-4675, November
Sponsor:Office of Naval Research, Washington, DC
noise (sound); exits; Melnikov process
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.