The stability of solutions to evolution equations with respect to small stochastic perturbations is considered. The stability of a stochastic dynamical system is characterized by the local stability index. The limit of this index with respect to infinite time describes the asymptotic stability of a stochastic dynamical system. Another limit of the stability index is given by the vanishing intensity of stochastic perturbations. A dynamical system is stochastically unstable when these two limits do not commute with each other. Several examples illustrate the thesis that there always exist such stochastic perturbations that render a given dynamical system stochastically unstable. The stochastic instability of quasi-isolated systems is responsible for the irreversibility of time arrow.
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| http://dx.doi.org/10.1103/PhysRevE.65.056118 | DOI Listing |
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