Multiplicative Levy noise in bistable systems

TL;DR

This paper investigates how multiplicative Lévy noise influences stochastic resonance in bistable systems, analyzing the effects of noise parameters and interpretation methods on system dynamics and resonance properties.

Contribution

It introduces a detailed analysis of multiplicative Lévy noise effects on bistable systems, considering both Stratonovich and Itô interpretations, and explores the resulting stochastic resonance behavior.

Findings

Mean first passage time varies with noise parameters.

Resonance peak height and position depend on noise intensity and interpretation.

System response exhibits stochastic resonance patterns influenced by noise characteristics.

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 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.