Resonant activation in discrete systems

The resonant activation phenomenon (RAP) in a discrete system is studied using the master equation formalism. We show that the RAP corresponds to a nonmonotonic behavior of the frequency dependent first passage time probability density function (PDF). An analytical expression for the resonant frequency is introduced, which, together with numerical results, helps understand the RAP behavior in the space spanned by the transition rates for the case of reflecting and absorbing boundary conditions. The limited range of system parameters for which the RAP occurs is discussed. We show that a minimum and a maximum in the mean first passage time can be obtained when both boundaries are absorbing. Relationships to some biological systems are suggested.