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Author
Frey, M. R. | Simiu, E.
Title
Noise-Induced Chaos and Phase Space Flux.
Coporate
National Institute of Standards and Technology, Gaithersburg, MD
Journal
Physica D, Vol. 63, 321-340, 1993
Keywords
noise (sound) | chaos | space flux | global perturbation methods | homoclinic orbit | asymptotic mean stationarity | sample-theoretic method
Abstract
We study the effect of additive noise on near-integrable second-order dynmaical systems whose unperturbed flows have homoxlinic or heteroclinic orbits. The noise is represented by a type of Shinozuka stochastic process capable of artitrarily closely approximating Gaussian noise with any specified spectrum. We derive a formula for the flux factor applicable for any asymptotic mean stationary excitation. This derivation shows that, to first order, the effect of the external excitation on the system is mediated by a linear filter associated with the system homocolinic or heteroclinic orbit. It also shows that the stationary mean distribution of the filtered excitation determines the average phase space flux. This is true for both random and nonrandom excitations and indicates that, for the dynamical systems considered here, these two classes of excitation play substantially equivalent roles in the promotion of chaos.