Melnikov Processes and Noise-Induced Exits From a Well.
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.
Sponsor:
Office of Naval Research, Washington, DC
Keywords:
building technology; dichotomous noise; dynamical
systems; function; stochastic dynamical systems
Abstract:
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.
Building and Fire Research Laboratory
National Institute of Standards and Technology
Gaithersburg, MD 20899