Numerical Investigation of Noise Enhanced Stability Phenomenon in a Time-Delayed Metastable System

The transient properties of a time-delayed metastable system subjected to the additive white noise are investigated by means of the stochastic simulation method. The noise enhanced stability phenomenon (NES) can be
observed in this system and the effect of the delay time on the NES shows a critical behaviour, i.e., there is a critical value of the delay time τ_c≈1, above which the time delay enhances the NES effect with the delay time increasing and below which the time delay weakens the NES effect as the delay time
increases.