Stochastic resonance in a time polo-delayed asymmetry bistable system driven by multiplicative white noise and additive color noise

Stochastic resonance (SR) in a time polo-delayed asymmetry bistable system driven by multiplicative white noise and additive color noise is investigated in this paper. First, the effective potential function is deduced based on probability density approach theory, small delay approximation theory and colored noise approximation theory. Second, the mean first-passage time (MFPT) which plays an important role in investigating on particles escape rate is derived and we find that the effect of additive color noise is more observable than that of multiplicative white noise on MFPT. Finally, influences of different parameters on SR are studied by signal-to-noise ratio (SNR). The analytic expression of SNR is derived and three-dimensional graphs of SNR with different parameters are obtained. We conclude that time delay τ and time delay strength e can suppress SR and that asymmetric item r has a non-monotone effect on SR. The results also suggest that adjusting the additive noise intensity Q is more sensitive than that of the multiplicative noise intensity D in controlling SNR.