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

In this paper, the Levy noise-induced transition in an underdamped asymmetric bistable system is discussed. Levy 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 gamma, asymmetric parameter r of system, stability index alpha, skewness parameters beta and noise intensity D on the stationary probability density are analyzed. The numerical simulation results show that the asymmetric parameter r, stability index alpha, skewness parameters beta and noise intensity D can induce the phase transition. However, the phase transition cannot be induced by the damped coefficient gamma.