Combined effects of asymmetry and noise correlation on the noise-enhanced stability phenomenon in a bistable system

We investigate the effects of asymmetry and noise correlation on the noise-enhanced stability (NES) phenomenon in an asymmetric bistable system driven by cross-correlated noises. The expressions for the average escape time from the left stable state T-L and from the right stable state T-R are derived. The results indicate that T-L and T-R, as a function of the multiplicative noise intensity D, show non-monotonic behavior with the presence of a maximum value in the cases of positive and negative correlation between noises, respectively. This is the distinguishing characteristic of the NES phenomenon. However, the additive noise cannot produce the NES effect. The NES effect for both states is enhanced as the cross-correlation strength between noises increases, but is weakened as the additive noise intensity increases, whereas the NES effect is enhanced for the left state and weakened for the right state as the asymmetry parameter increases. Moreover, the validity of the analytical approximation is confirmed by stochastic simulations.