Abstract

Properties of dynamical behavior of nonlinear systems exhibiting chaos are investigated, under small random perturbations. Chaotic properties of deterministic systems modeled by a one-dimensional mapping are analyzed when the system is perturbed by a multiplicative and an additive noise. Stochastic versions of invariant measure and Lyapunov exponent are calculated and are comparatively discussed with deterministic ones, from the viewpoint of conservation of chaotic properties under small random perturbations. Finally, a different type of stochastic systems is shown to be equivalent to a deterministic system with chaotic behavior in some stochastic sense.

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