Stochastic Resonance of a Periodically Driven Bistable System with Two Different Kinds of Time Delays

In this paper, we study the phenomenon of stochastic resonance (SR) in a periodically driven bistable system with correlations between multiplicative and additive white noise terms when there are two different kinds of time delays existed in the deterministic and fluctuating forces, respectively. Using the small time delay approximation and the theory of signal-to-noise ratio(SNR) in the adiabatic limit, the expression of SNR is obtained. The effects of the delay time tau in the deterministic force,and the delay time theta in the fluctuating force on SNR are discussed. Based on the numerical computation, it is found that: (i)There appears a reentrant transition between one peak and two peaks and then to one peak again in the curve of SNR when the value of the time delay theta is increased.(ii)SR can be realized by tuning the time delay tau or theta with fixed noise, i.e., delay-induced stochastic resonance (DSR) exists.