Transitions to Chaos Induced by Additive and Multiplicative Noise.
Transitions to Chaos Induced by Additive and
Simiu, E.; Frey, M. R.
Towards the Harnessing of Chaos, Elsevier Science B.V.,
NY, Yamaguti, M., Editor(s), 405-408 pp, 1994.
Sponsor: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.