Escape for System with Non-Fluctuating Potential Barrier Only Driven by Three-State Noise

We study the escape for the mean first passage time (MFPT) over a potential barrier for a system with non-fluctuating potential barrier and only driven by a three-state noise. It is shown that in some circumstances, the three-state noise can induce the resonant activation for the MFPT over the potential barrier; but in other circumstances, it can not. There are three resonant activations for the MFPT over the potential barrier, which are respectively as the functions of the transition rates of the three-state noise.