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Center for Nonlinear Studies |
Systems driven by additive or multiplicative dichotomous Markov noise appear in a wide variety of physical and mathematical models. We review here the main features of these models, with an emphasis on exactly-solvable situations. In particular, it has escaped attention till recently that the standard results for the long-time properties of such systems cannot be applied when unstable fixed points are crossed in the asymptotic regime. We show how calculations have to be modified to deal with these cases and present a few applications -- the hypersensitive transport, the rocking ratchet, and the stochastic Stokes' drift. These results reinforce the impression that dichotomous noise can be put on a par with Gaussian white noise as far as obtaining analytic results is concerned. Moreover, they convincingly illustrate the interplay between noise and nonlinearity in generating nontrivial behaviors of nonequilibrium systems and point to interesting applications.