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The European Physical Journal Special Topics

, Volume 216, Issue 1, pp 133–138 | Cite as

Stationary states in bistable system driven by Lévy noise

  • O.Yu. SliusarenkoEmail author
  • D.A. Surkov
  • V.Yu. Gonchar
  • A.V. Chechkin
Regular Article

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.

Keywords

Probability Density Function European Physical Journal Special Topic Noise Intensity Bistable System Quartic Potential 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© EDP Sciences and Springer 2013

Authors and Affiliations

  • O.Yu. Sliusarenko
    • 1
    Email author
  • D.A. Surkov
    • 2
  • V.Yu. Gonchar
    • 1
  • A.V. Chechkin
    • 1
    • 3
  1. 1.Akhiezer Institute for Theoretical Physics National Science Center “Kharkiv Institute of Physics and Technology”KharkivUkraine
  2. 2.Karazin National UniversityKharkivUkraine
  3. 3.Institute for Physics and Astronomy University of PotsdamPotsdam-GolmGermany

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