In this paper, the first-passage behavior of under-damped asymmetric bistable system driven by Lévy noise is studied. The two aspects considered are the mean first-passage time (MFPT) and the distribution of first-passage time in two opposite directions. To begin with, using the Janicki–Weron algorithm to generate Lévy noise, the system driven by Lévy noise is simulated through the fourth-order Runge–Kutta algorithm. Then the first-passage time of [Formula: see text] response tracks is calculated, and the MFPT and the distribution of first-passage time are obtained. Finally, the influence of Lévy noise and system parameters on MFPT and the distribution of first-passage time are analyzed. Moreover, the noise enhanced stability (NES) effect is found.
The mean first-passage time for an asymmetric bistable system driven by multiplicative colored and additive white noise with a correlated noise