Stochastic resonance induced by a multiplicative periodic signal in the gene transcriptional regulatory system with correlated noises

This paper investigates the stochastic resonance (SR) induced by a multiplicative periodic signal in the gene transcriptional regulatory system with correlated noises. The expression of the signal-to-noise ratio (SNR) is derived. The results indicate that the existence of a maximum in SNR vs. the additive noise intensity \alpha, the multiplicative noise intensity D and the cross-correlated noise intensity \lambda is the identifying characteristic of the SR phenomenon and there is a critical phenomenon in the SNR as a function of \lambda , i.e., for the case of smaller values of noise intensity (\alpha or D), the SNR decreases as \lambda increases; however, for the case of larger values of noise intensity (\alpha or D), the SNR increases as \lambda increases.