Multi-Resonant-Activation for a System Only Driven by Multi-State Noise

We consider the escape of the particles over fluctuating potential barrier for a system only driven by a multi-state noise. It is shown that, the noise can make the particles escape over the fluctuating potential barrier in some circumstances; but in other circumstances, it can not. If the noise can make the particle escape over the fluctuating potential barrier, the mean firstpassage time (MFPT) can display the phenomenon of multi-resonant-activation. For this phenomenon, there are two kinds of resonant activation to appear. One is resonant activation for the MFPTs as the function of the flipping rates of the fluctuating potential barrier; the other is that for the MFPTs as the functions of the transition rates of the multi-state noise.