Escape rate in the gene transcriptional regulatory system with time delay

Abstract

The escape rate in the gene transcriptional regulatory system with time delay in the presence of cross-correlation noises is studied. The expression of the escape rate is derived under the condition of small delay time. Based on the escape rate, we investigated the effects of both cross-correlation intensity (λ) and delay time (τ) on the escape rate. Our results indicate that: (i) under positively correlated noises action (i.e. λ> 0), the escape rate exhibits one minimum value as the intensities of the multiplicative and additive noises vary, namely the suppression effect. However, for the case of uncorrelated noises (λ=0) and negatively correlated noises (λ<0), the suppression phenomenon disappears. (ii) λ and τ have opposite effects on the escape rate of the system, i.e. under positively correlated noises action, an increase of λ can intensify the suppression of the escape rate, but an increase of τ can weaken the suppression of the escape rate.