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Melnikov Necessary Condition for Noise-Induced Escapes.


pdf icon Melnikov Necessary Condition for Noise-Induced Escapes. (392 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.