Multiplicative Levy noise in bistable systems

Details Multiplicative Levy noise in bistable systems Multiplicative Levy noise in bistable systems

2012-02-14

arxiv.org/abs/1202.3023v1

Eur. Phys. J. B85 (2012) 65

Physics

Condensed Matter

Statistical Mechanics

8 pages, 6 figures

Scientific paper

10.1140/epjb/e2012-30003-9

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 L\'evy distribution. The noise is multiplicative: its intensity depends on the process variable like |x|^{-\theta}. The Stratonovich and It\^o interpretations of the stochastic integral are taken into account. The mean first passage time is calculated as a function of \theta for different values of the stability index \alpha 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 \alpha, \theta\ and size of the barrier are discussed. Both height and position of the peak strongly depends on \theta\ and on a specific interpretation of the stochastic integral.

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