Stationary States in Bistable System Driven by Lévy Noise

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 with 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 potential's depth and Lévy noise parameters.

Accepted to EPJST

References in corpus (3)

• The problem of analytical calculation of barrier crossing characteristics for Levy flights
• Stationary states in Langevin dynamics under asymmetric Lévy noises
• Steady-State Lévy Flights in a Confined Domain

Cited by in corpus (5)

• Fractional Underdamped Langevin Dynamics: Retargeting SGD with Momentum under Heavy-Tailed Gradient Noise
• Multimodal stationary states in symmetric single-well potentials driven by Cauchy noise
• Stationary states in 2D systems driven by bi-variate Lévy noises
• Escape from bounded domains driven by multi-variate $\alpha$-stable noises
• Asymmetric Heavy Tails and Implicit Bias in Gaussian Noise Injections