  The resonant activation phenomenon (RAP) in a discrete system is studied
using the master equation formalism. We show that the RAP corresponds to a
non-monotonic 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 (MFPT) can be obtained when both
boundaries are absorbing. Relationships to some biological systems are
suggested.
