Mean first-passage time of general bistable systems driven by white noise excitations

The mean first-passage time (MFPT) of one-dimensional and multi-dimensional bistable systems with weak damping driven by white noise excitations is studied. The Pontryagin equation governing the MFPT is established based on the stochastic averaging method and the MFPT is obtained through solving the Pontryagin equation together with its boundary conditions. By comparing the theoretical results and the results from a Monte Carlo simulation, it is verified that the MFPT can be predicted quite well using the proposed method. Furthermore, it is shown that the MFPT decreases when the density of the random excitations or the correlative strength of two excitations increases.