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Transitions to Chaos Induced by Additive and Multiplicative Noise.

pdf icon Transitions to Chaos Induced by Additive and Multiplicative Noise. (166 K)
Simiu, E.; Frey, M. R.

Towards the Harnessing of Chaos, Elsevier Science B.V., NY, Yamaguti, M., Editor(s), 405-408 pp, 1994.


Office of Naval Research, Washington, DC


noise (sound); equations; chaos


For a class of multistable systems, deterministic and stochastic chaos are closely related mathematically; a necessary condition for the occurrence of noise-induced chaos with sensititive dependence on initial conditions can be derived from the generalized Melnikov function. Proof that this condition is applicable requires the approximate representation of the noise in the form of a modified Shinozuka process or other uniformly continuous and uniformly bounded processes. Additive and/or multiplicative Gaussian noise with any spectral density can be accommodated, as can other types of noises, including shot noise and non-Gaussian noise. We review recent results, including a successful verification of our Melnikov-based approach against results based on a solution of the Fokker-Planck equation. We conclude by briefly describing ongoing research.