Stochastic Resonance in a Gene Transcriptional Regulatory System with Time Delay

We study the stochastic resonance (SR)　phenomenon in a time-delayed gene transcriptional regulatory system　under the simultaneous action of a multiplicative noise and an　additive noise and a weak periodic signal. The expression of the　signal-to-noise ratio R_SNR is obtained by applying the
two-state theory in adiabatic limit under the condition of small　delay time. The effects of delay time and intensity of the　correlation between multiplicative and additive noise on R_SNR are discussed. It is found that the delay time τ enhances　the SR of the system. The correlation intensity λ enhances　the SR in the R_SNR-D plot (D denotes the multiplicative　noise intensity), but weakens the SR in the R_SNR-α　plot (α denotes the additive noise intensity).