Bounded noise enhanced stability and resonant activation

We investigate the escape problem of a Brownian particle over a potential barrier driven by bounded noise, which is different form the common unbounded noise. Some novel stochastic phenomena and results are founded. For weak frequency of bounded noise, the mean first passage time (MFPT) shows a non-monotonic dependence on the intensity of white noise. One remarkable behavior is the phenomenon of co-occurrence of noise-enhanced stability and resonant activation. Another novel finding is that the position of minimum of MFPT about frequency shows monotone non-decreasing or non-increasing function with the variation of amplitude of bounded noise, while the minimum of MFPT monotonously depends on the amplitude of bounded noise. More important, we uncover the relationship of the parameters of bounded noise which induce the occurrence of the phenomenon of resonant activation. Besides, resonant activation can also be induced by simplified bounded noise, called sine-Wiener noise. The behaviors presented in our work driven by bounded noise show distinctive features compared with the ones inspired by the common noise.