Phase transitions and the mean first passage time of an asymmetric bistable system with non-Gaussian Lévy noise

This paper aims to investigate an asymmetric bistable system driven by non-Gaussian Lévy noise. The stationary probability density functions are obtained by the Grünwald-Letnikov scheme, and the effects of noise intensity and stability index on the stationary probability density are examined. Phase transitions can be observed though a qualitative change of the stationary probability distribution, which indicates that the phase transitions are induced by the asymmetric parameter and the stability index of Lévy noise. Additionally, the mean first passage time is considered, and different mechanisms for the effects of asymmetric parameter, noise intensity and stability index on first passage time are also obtained.