Effects of time delay and noise correlation on noise enhanced stability and resonant activation in a periodically modulated bistable system

This work analyzes numerically the effects of delay time τ and cross-correlation strength between noises λ on the phenomena of noise enhanced stability (NES) and resonant activation (RA) in a periodically modulated bistable system. The simulation results indicate that: (i) multiplicative noise can produce the NES effect only for the larger λ, while additive noise always induces the NES effect; (ii) for the NES phenomenon induced by additive noise, there is a characteristic value of τ, below which the increasing of τ enhances it and above which the effect of τ reverses; however, the increasing of τ can only enhance the NES effect induced by multiplicative noise; (iii) increasing λ weakens the NES effect induced by additive noise and strengthens that induced by multiplicative noise; and (iv) the RA effect becomes more and more pronounced while the RA minimum of the mean first-passage time increases with the increase of λ or τ. (paper)