Noise-Induced Sensitivity to Initial Conditions
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 discussed.
KeywordsUnstable Manifold Shot Noise Multiplicative Noise Simple Zero Multistable System
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