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Melnikov Processes and Noise-Induced Exits From a Well.

pdf icon Melnikov Processes and Noise-Induced Exits From a Well. (751 K)
Simiu, E.; Frey, M. R. R.

Paper 9809;

Journal of Engineering Mechanics, Vol. 122, No. 3, 263-270, March 1996.


Office of Naval Research, Washington, DC


building technology; dichotomous noise; dynamical systems; function; stochastic dynamical systems


For a wide class of near-integrable systems with additive or multiplicative noise the mean zero upcrossing rate for the stochastic system's Melnikov process, provides an upper bound for the system's mean exit rate. Comparisons between Melnikov process and mean exit rate show that in the particular case of additive white noise this upper bound is weak. For systems excited by processes with tail-limited distributions, the stochastic Melnikov approach yields a simple criterion guaranteeing the nonoccurrence of chaos. This is illustrated for the case of excitation by square-wave, coin-toss dichotomous noise. Finally, we briefly review applications of the stochastic Melnikov approach to a study of the behavior of wind-induced fluctuating currents over a corrugated ocean floor; the snap-through of buckled columns with continuous mass distribution and distributed random loading; and open-loop control of stochastically excited multistable systems.