Escape over a fluctuating barrier with additive and multiplicative noise.

The mean first passage time (MFPT) over the fluctuating potential barrier is investigated in the presence of additive and multiplicative noises. It is shown that the MFPT over the fluctuating potential barrier displays a resonant activation (RA). The effect of the additive and multiplicative noises and the correlation between them on the RA is that the additive and multiplicative noises can weaken the RA; but the correlation between them can enhance it. The susceptibility of the RA to the multiplicative noise is far larger than that to the additive one. In addition, we find that the transition rate (i.e., the inverse of the MFPT) over the fluctuating potential barrier can be suppressed by the positive correlation and show a minimum as the function of the noises' strengths.