Noise-induced transition in an underdamped asymmetric bistable system driven by Lévy noise

Abstract

In this paper, the Lévy noise-induced transition in an underdamped asymmetric bistable system is discussed. Lévy noise is generated  through the Janicki–Weron algorithm and the numerical solutions of system equation is obtained by the fourth-order Runge–Kutta method. Then the stationary probability density functions are obtained by solving the equation of system. The influence of the damped coefficient [Formula: see text], asymmetric parameter r of system, stability index [Formula: see text], skewness parameters [Formula: see text] and noise intensity D on the stationary probability density are analyzed. The numerical simulation results show that the asymmetric parameter r, stability index [Formula: see text], skewness parameters [Formula: see text] and noise intensity D can induce the phase transition. However, the phase transition cannot be induced by the damped coefficient [Formula: see text].