Noise-Induced Sensitivity to Initial Conditions.
Noise-Induced Sensitivity to Initial Conditions.
(429 K)
Simiu, E.; Frey, M. R. R.
Fluctuations and Order: The New Synthesis.
Proceedings. Chapter 6. 1996, Springer, New York, NY,
Millonas, M., Editor(s), 81-90 pp, 1996.
Sponsor:
Office of Naval Research, Washington, DC
Keywords:
building technology; chaos; Melnikov function; noise
(sound); ocean engineering; sensitivity to initial
conditions; stochastic equations; structural engineering
Abstract:
Deterministic chaos and noise-induced basin hopping are
closely related in a broad class of multistable
dynamical systems. A necessary condition for
sensitivity to initial conditions, based on the
generalized Melnikov function and originally derived for
deterministic systems, can be extended to systems
excited by noise. This extension involves the
representation of noise processes as sums of terms with
random parameters. Gaussian noise and shot noise can be
accommodated for both additive and multiplicative
excitations. Our extension of the Melnikov approach
shows that, for the class of noise-excited systems being
considered, basin hopping implies sensitivity to initial
conditions. Applications of this approach to
noise-excited systems are discusses.
Building and Fire Research Laboratory
National Institute of Standards and Technology
Gaithersburg, MD 20899