Role of the initial conditions on the enhancement of the escape time in static and fluctuating potentials

We present a study of the noise driven escape of an overdamped Brownian particle moving in a cubic potential profile with a metastable state. We analyze the role of the initial conditions of the particle on the enhancement of the average escape time as a function of the noise intensity for fixed and fluctuating potentials. We observe the noise enhanced stability effect for all the initial unstable states investigated. For a fixed potential we find a peculiar initial condition x c which separates the set of the initial unstable states in two regions: those which give rise to divergences from those which show nonmonotonic behavior of the average escape time. For fluctuating potential at this particular initial condition and for low noise intensity we find large fluctuations of the average escape time. behavior of the mean escape time as a function of noise intensity is a noise-induced effect for nonlinear nonequilibrium systems with metastable states. In this work we analyzed the role of the initial conditions on the enhancement of the escape time from initial unstable states for a cubic potential. We obtain NES effect for static and periodical fluctuating potential and an enhancement of the NES effect for initial positions between the maximum of the potential well and the cross point x c . We find also large fluctuations of the average escape time as a function of both the amplitude and the frequency of the sinusoidal force for low noise intensity, due to the different dynamical regimes experienced by the Brownian particle. Our results obtained for a particle moving in a cubic potential are quite general, because we always obtain NES effect when a particle is initially located just to the right of a local potential maximum, with a local minimum in its left side and the global escape region in its right side.