Melnikov Necessary Condition for Noise-Induced Escapes.
Melnikov Necessary Condition for Noise-Induced Escapes.
(494 K)
Simiu, E.; Frey, M. R.; Hagwood, C.
International Association for Civil Engineering
Reliability and Risk Analysis (CERRA). International
Conference on ICASP, 7th Proceedings. Applications of
Statistics and Probability. Civil Engineering
Reliability and Risk Analysis. July 10-13, 1995, Paris,
France, A.A. Balkema, Rotterdam, Lemaire, M.; Favre, J.
L.; Mebarki, A., Editor(s)(s), 1137-1142 pp, 1995.
Sponsor:
Office of Naval Research, Washington, DC
Keywords:
noise (sound); Melnikov function; equations; escape
means
Abstract:
For a wide class of nonlinear multistable deterministic
systems, a necessary condition for the occurrence of
chaos - and jumps between phase space regions associated
with potential wells - is that the system's Melnikov
function have simple zeros. The work presented in this
paper is based on our extension of the Melnikov-based
approach to a class of nonlinear stochastic differential
equations with additive or multiplicative noise. The
mean zero upcrossing rate for the stochastic system's
Melnikov process is a weak upper bound for the system's
mean escape rate. For systems excited by processes with
tail-limited distributions the stochastic Melnikov
approach yields a simple criterion guaranteeing the
non-occurrence of chaos. This is illustrated for
excitation by square wave, coin-toss dichotomous noise.
Building and Fire Research Laboratory
National Institute of Standards and Technology
Gaithersburg, MD 20899