Multiplicative Lévy noise in bistable systems
Institute of Nuclear Physics, Polish Academy of
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Received in final form: 13 January 2012
Published online: 13 February 2012
Stochastic motion in a bistable, periodically modulated potential is discussed. The system is stimulated by a white noise increments of which have a symmetric stable Lévy distribution. The noise is multiplicative: its intensity depends on the process variable like |x|−θ. The Stratonovich and Itô interpretations of the stochastic integral are taken into account. The mean first passage time is calculated as a function of θ for different values of the stability index α and size of the barrier. Dependence of the output amplitude on the noise intensity reveals a pattern typical for the stochastic resonance. Properties of the resonance as a function of α, θ and size of the barrier are discussed. Both height and position of the peak strongly depends on θ and on a specific interpretation of the stochastic integral.
Key words: Statistical and Nonlinear Physics
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2012