Noise enhanced stability effect in a metastable system with two different kinds of time delays and cross-correlated noises

We numerically investigate the influences of the time delay tau simultaneously existing in both the deterministic and fluctuating forces, the time delay tau(r) existing only in the fluctuating force and the cross-correlation strength lambda on the enhancement of the mean first-passage time ( MFPT) as a function of the additive D and the multiplicative alpha noise intensities in a metastable system. The results indicate that both the multiplicative and additive noises can induce the noise-enhanced stability (NES) effect. An increase of lambda can enhance or weaken the NES effect induced by the additive noise, depending on the value of tau. However, it weakens the NES effect induced by the multiplicative noise with a suppression of the effect of lambda caused by increasing tau. The tau-induced critical behavior on both NES effects can be observed, i.e. an increase of tau can enhance or restrain the NES effects induced by the two kinds of noises. With an increase of lambda and tau, MFPT versus D shows a transition from one peak to two peaks and finally one peak, implying the multiple NES effect caused by lambda and tau. An increase of tau(r) can enhance the NES effect induced by the additive noise and weaken the NES effect induced by the multiplicative noise.