Exits in Second-Order Nonlinear Systems Driven by Dichotomous Noise.
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.
Sponsor:
Office of Naval Research, Arlington, VA
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.
Building and Fire Research Laboratory
National Institute of Standards and Technology
Gaithersburg, MD 20899