Effects of Lévy Noise on a bistable Duffing System

Abstract

This paper numerically investigates the mean first passage time (MFPT) and phase transition of a bistable Duffing system driven by Lévy 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 Lévy noise parameters on the stationary probability densities are discussed. The results indicate that the stability index, noise intensity and skewness parameter of Lévy 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 Lévy and Gaussian noise can be observed.