  The overdamped motion of a Brownian particle in randomly switching piece-wise
metastable linear potential shows noise enhanced stability (NES): the noise
stabilizes the metastable system and the system remains in this state for a
longer time than in the absence of white noise. The mean first passage time
(MFPT) has a maximum at a finite value of white noise intensity. The analytical
expression of MFPT in terms of the white noise intensity, the parameters of the
potential barrier, and of the dichotomous noise is derived. The conditions for
the NES phenomenon and the parameter region where the effect can be observed
are obtained. The mean first passage time behaviours as a function of the mean
flipping rate of the potential for unstable and metastable initial
configurations are also analyzed. We observe the resonant activation phenomenon
for initial metastable configuration of the potential profile.
