Effects of L\'evy Noise on a bistable Duffing System

TL;DR

This study explores how Le9vy stable noise influences the phase transition and mean first passage time in a bistable Duffing system, revealing distinct effects compared to Gaussian noise through numerical simulations.

Contribution

It provides a detailed numerical analysis of Le9vy noise effects on a bistable Duffing system, highlighting how noise parameters induce phase transitions and alter MFPT.

Findings

Le9vy noise parameters can trigger phase transitions in the system.

The stability index and skewness significantly affect MFPT.

Distinct behaviors are observed between Le9vy and Gaussian noise effects.

Abstract

This paper numerically investigates the mean first passage time (MFPT) and phase transition of a bistable Duffing system driven by L\'evy stable noise, which can reduce to the common Gaussian noise with the stability index 2. We obtain the stationary probability density functions by using Monte Carlo method to describe the change in distribution law and the influences of L\'evy noise parameters on the stationary probability densities are discussed. The results indicate that the stability index, noise intensity and skewness parameter of L\'evy noise can induce the phase transition behaviors (namely, the qualitative change of stationary probability density function). Furthermore, the MFPT is calculated as functions of different parameters, which implies that the effects of the stability index, noise intensity and the skewness parameter on MFPT are quite different, and apparent distinctions between L\'evy and Gaussian noise can be observed.