Enhancement of the escape time in metastable states with colored noise

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We present a study of the escape time from a metastable state in the presence of colored noise, generated by Ornstein-Uhlenbeck process. We analyze the role of the correlated noise and of unstable initial conditions of an overdamped Brownian particle on the enhancement of the average escape time as a function of the noise intensity. We observe the noise enhanced stability (NES) effect for all the initial unstable states and for all values of the correlation time τc investigated. We can distinguish two dynamical regimes characterized by: (a) a weak correlated noise and (b) a strong correlated noise, depending on the value of τc with respect to the relaxation time. With increasing τc we find: (i) a shift of the maximum of the average escape time towards higher values of noise intensity and an enhancement of the value of this maximum; (ii) a broadening of the NES region, which becomes very large in the strong colored noise regime; (iii) in this regime (b), the absence of the peculiar initial condition xc which separates the set of the initial unstable states lying into the divergency region from those which give only a nonmonotonic behavior of the average escape time.