Relaxation Time for an Optical Bistable System Subjected to Color Noises

The relaxation time T of an optical bistable system with cross–correlated color noises and small time delay is investigated. Using the Novikov theorem and Fox approach, the steady probability distribution is obtained. The expression of T is derived using the Stratonovich decoupling ansatz formalism. It is found that the relaxation time T increases with the increasing cross–correlation time τ₀ between the two noises or the self–correlation time τ₁ of the multiplicative noise, but decreases with the increasing self–correlation time τ₂ of the additive noise. T decreases with the increasing correlation intensity λ or the multiplicative noise intensity Q, but increases with the increasing additive noise intensity D. There exists a peak in the curve of T versus delay time τ.