Effects of cross correlated noises on the mean first-passage time of optical bistable system

The effects of multiplicative colored noise and additive white noise on the mean first-passage time ( MFPT) T+ (x(s1) -> x(s2)) and T- (x(s2) -> x(s1)) of an optical bistable system are investigated. The approximate Fokker-Planck equation is obtained based on the Novikov theorem and the Fox approach. The expression of MFPT is obtained in the steepest-descent approximation. Numerical results show that ( I) the multiplicative noise intensity Q and additive noise intensity D play the same roles in T+ (x(s1) -> x(s2)) but different roles in T- (x(s1) -> x(s2)); (2) T+ (x(s1) -> x(s2)) increases with the increase of the self-correlation time tau but decreases with the increase of the correlation intensity lambda; (3) T- (x(s2) -> x(s1)) decreases with tau increasing, but increases with lambda increasing.