Abstract
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 RSNR 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 RSNR 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 RSNR - D plot (D denotes the multiplicative noise intensity), but weakens the SR in the RSNR - α plot (α denotes the additive noise intensity).
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