Enhancement of the escape time in metastable states with colored noise

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 $\tau_c$ 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 $\tau_c$ with respect to the relaxation time. With increasing $\tau_c$ 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 $x_c$ 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.