- Author
- Simiu, E. | Hagwood, C.
- Title
- Exits in Second-Order Nonlinear Systems Driven by Dichotomous Noise.
- Coporate
- National Institute of Standards and Technology, Gaithersburg, MD
- Sponsor
- Office of Naval Research, Arlington, VA
- Contract
- ONR-GRANT-N00014-0248
- Book or Conf
- Computation of Stochastic Mechanics, 2nd International Conference. Proceedings. June 13-15, 1994, Balkema, Rotterdam, Athens, Greece, Spanos, P. D., Editors, 395-401 p., 1995
- Keywords
- building technology | chaos | dichotomous noise | dynamical systems | exit time | Melnikov function | stochastic process
- Abstract
- 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.