Eur. Phys. J. Special Topics 216, 133-138 (2013)
https://doi.org/10.1140/epjst/e2013-01736-0

Regular Article

Stationary states in bistable system driven by Lévy noise

¹ Akhiezer Institute for Theoretical Physics National Science Center “Kharkiv Institute of Physics and Technology”, Akademichna st. 1, Kharkiv 61108, Ukraine
² Karazin National University, Svobody sq. 4, Kharkiv 61022, Ukraine
³ Institute for Physics and Astronomy University of Potsdam, 14476 Potsdam-Golm, Germany

^a e-mail: aslusarenko@kipt.kharkov.ua

Received: 30 November 2012
Revised: 6 December 2012
Published online: 31 January 2013

Abstract

We study the properties of the probability density function (PDF) of a bistable system driven by heavy tailed white symmetric Lévy noise. The shape of the stationary PDF is found analytically for the particular case of the Lévy index α = 1 (Cauchy noise). For an arbitrary Lévy index we employ numerical methods based on the solution of the stochastic Langevin equation and space fractional kinetic equation. In contrast to the bistable system driven by Gaussian noise, in the Lévy case, the positions of maxima of the stationary PDF do not coincide with the positions of minima of the bistable potential. We provide a detailed study of the distance between the maxima and the minima as a function of the depth of the potential and the Lévy noise parameters.