Abstract
Based on the universal transcriptional regulatory model proposed by Smolen et al.in 1998, we have studied the combined effects of cross-correlation noise, multiplicative periodic signal and time delay through modifying the ordinary differential equation with time evolution in gene transcriptional regulatory system. The expression of signal-to-noise ratio (SNR) is derived by applying the two-state theory in adiabatic limit and approximate analytical method for small time delay. The effects of multiplicative noise intensity, additive noise intensity, cross-correlation noise intensity and time delay on SNR are discussed by numerical calculation and graphical analysis. The results indicate that when the SNR is a function of multiplicative noise intensity, the peak value of the SNR rises as time delay increases; when SNR is a function of additive noise intensity, the value of SNR ascends as time delay increases; when SNR is a function of cross-correlation noise intensity, the peak value of SNR goes up with time delay increased. So when SNR is the function of multiplicative noise intensity, additive noise intensity and cross-correlation noise intensity respectively, time delay enhances the stochastic resonance.
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