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Exits in Second-Order Nonlinear Systems Driven by Dichotomous Noise.

pdf icon Exits in Second-Order Nonlinear Systems Driven by Dichotomous Noise. (402 K)
Simiu, E.; Hagwood, C.

Computation of Stochastic Mechanics, 2nd International Conference. Proceedings. June 13-15, 1994, Athens, Greece, Balkema, Rotterdam, Spanos, P. D., Editor(s), 395-401 pp, 1995.


Office of Naval Research, Arlington, VA


building technology; chaos; dichotomous noise; dynamical systems; exit time; Melnikov function; stochastic process


We consider a wide class of lightly damped second-order differential equations with double-well potential and small coin-toss square wave dichotomous noise. The behavior of these systems is similar to that of 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 exists from the wells. This similarity suggests the application to the stochastic systems of a Melnikov-based approach originally developed for deterministic systems. This approach accommodates both additive and multiplicative noise. It yields a generalized Melnikov function which is used to obatin (i) a simple condition guaranteeing the non-occurrence of exits from a well, and (ii) weak lower bounds for the mean time of exit from a well and for the probability that exits will not occur during a specified time interval.