First-passage time statistics in a bistable system subject to Poisson white noise by the generalized cell mapping method

The first-passage time statistics in a bistable system subject to Poisson white noise is studied by using the generalized cell mapping method. Specifically, an approximate solution for the first-passage time statistics in a second-order bistable system is developed by analyzing the motions in double-well potential and the global dynamics in phase space. Both symmetric and asymmetric cases have been investigated, and the effects of noise intensity and mean arrival rate of impulse on the first-passage time statistics are discussed respectively. It shows that the effect of Poisson white noise excitation on the first-passage time is quite different from that of the Gaussian one. With the same noise intensity, Poisson white noise can make for a faster first-passage.