Eur. Phys. J. B (2012) 85: 65
https://doi.org/10.1140/epjb/e2012-30003-9

Regular Article

Multiplicative Lévy noise in bistable systems

Institute of Nuclear Physics, Polish Academy of Sciences, Kraków PL-31-342, Poland

^a e-mail: tomasz.srokowski@ifj.edu.pl

Received: 3 January 2012
Received in final form: 13 January 2012
Published online: 13 February 2012

Abstract

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.