Dynamical entropy for systems with stochastic perturbation

Details Dynamical entropy for systems with stochastic perturbation Dynamical entropy for systems with stochastic perturbation

1999-05-27

arxiv.org/abs/chao-dyn/9905041v2

Phys. Rev. E 62 (2000) 2018

Nonlinear Sciences

Chaotic Dynamics

REVTeX 18 pages, 9 figures Revised section II, some minor improvements and corrections

Scientific paper

10.1103/PhysRevE.62.2018

Dynamics of deterministic systems perturbed by random additive noise is characterized quantitatively. Since for such systems the KS-entropy diverges we analyse the difference between the total entropy of a noisy system and the entropy of the noise itself. We show that this quantity is non negative and in the weak noise limit is conjectured to tend to the KS-entropy of the deterministic system. In particular, we consider one-dimensional systems with noise described by a finite-dimensional kernel, for which the Frobenius-Perron operator can be represented by a finite matrix.

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