Levy Noise-Induced Effects in Underdamped Asymmetric Bistable System

This paper aims to explore the Levy noise-induced effects in underdamped asymmetric bistable system. Levy noise is generated by Janicki-Weron algorithm which is different from the usual Gaussian noise. The numerical solutions of system equation are obtained by the fourth-order stochastic Runge-Kutta algorithm. Then the quasi-steady-state probability density (QSPD) is obtained by solving the equation of system, and the stochastic resonance (SR) is determined by the classical measure of signal-to-noise ratio (SNR). The influence of various parameters of the Levy noise and the system parameters on QSPD and SNR is discussed. Noise-induced transitions occur by varying the parameters of the Levy noise and the driven system. Moreover, within certain limits, the larger value of the stability index alpha of Levy noise, signal amplitude A, and the absolute values of asymmetric parameter r can give rise to the SR phenomenon. On the contrary, the larger values of skewness parameters beta of Levy noise and damping parameter gamma further weaken the occurrence of the SR phenomenon in the given system.