Effects of Time Delay on Stability of an Unstable State in a Bistable System with Correlated Noises

Effects of time delay on stability of an unstable state in a time-delayed bistable system are investigated.The analytic expression of the transition rate W(x_(u),τ)from unstable state xu to stable state x+is derived.The numerical calculation results of W(x_(u),τ)indicate that W(x_(u),τ)decreases with the increasing multiplicative noise intensity,the additive noise intensi by and the strength of correlations between the multiplicative and the additive noise increase,but W(x_(u),τ)increases with increasing delay time.Namely,the multiplicative noise,the additive noise and the correlations between the multiplicative and the additive noises enhance the stability of the unstable state in the time-delayed bistable system but the stability is weakened by time delay.