Effects of time delay on the statistical fluctuations for a bistable system driven by cross-correlated noises

We study the effects of time delay on the normalized correlation function C(s) and the associated relaxation time T-c for a bistable system with correlations between multiplicative and additive white noises under the condition of small time delay. Using the projection operator method, the expressions of T-c and C(s) are obtained. Based on numerical computations, it is found that the delay time tau slows down the rate of fluctuation decay of dynamical variable for the presence of positive feedback intensity (epsilon > 0), while speeds up the rate of fluctuation decay of dynamical variable for the presence of negative feedback intensity (epsilon < 0). The effects of the delay time tau on the T-c and C(s) are entirely opposite for epsilon > 0 and epsilon < 0.