Melnikov Process for Stochastically Perturbed, Slowly Varying Oscillators: Application to a Model of Wind-Driven Coastal Currents.
Melnikov Process for Stochastically Perturbed, Slowly
Varying Oscillators: Application to a Model of
Wind-Driven Coastal Currents.
(650 K)
Simiu, E.
Journal of Applied Mechanics, Vol. 63, 429-435, June
1996.
Sponsor:
Office of Naval Research, Washington, DC
Keywords:
chaos; currents; dynamical systems; mean exit time;
melnikov function; ocean engineering; stochastic
differential equations; wind engineering
Abstract:
The stochastic Melnikov approach is extended to a class
of slowly varying dynamical systems. It is found that
(1) necessary conditions for chaos induced by stochastic
perturbations depend on the excitation spectrum and the
transfer function in the expression for the Melnikov
transform; (2) the Melnikov approach allows the
estimation of lower bounds for (a) the mean time of exit
from preferred regions of phase space, and (b) the
probability that exits from those regions cannot occur
during a specified time interval. For a system modeling
wind-induced currents, the deterministic Melnikov
approach would indicate that chaotic transport cannot
occur for certain parameter ranges. However, the more
realistic stochastic Melnikov approach shows that, for
those same parameter ranges, the necessary conditions
for exits during a specified time interval are satisfied
with probabilities that increase as the time interval
increases.
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