تأثیر تاخیر زمانی در یک شبکه تنظیم مقررات تصادفی

In this paper, stationary probability distribution (SPD), mean first passage time (MFPT) and stochastic resonance (SR) phenomenon of an abstract model of the Myc/E2F/MiR-17-92 network with time delay and cross-correlation noise sources are investigated. The impacts of time delay τ, additive and multiplicative noise intensities Q and D, and cross-correlation intensity λ between noises on the SPD, MFPT, and SNR are discussed, respectively. Research results show that: (i) the high protein level (or ON) state is enhanced (or weaken) by the τ (or λ); (ii) the MFPT as a function of Q or D exhibits a maximum, which is the signature of the noise enhanced stability (NES) of the ON state. The stability of the ON state can also enhance (or weaken) by the λ (or τ); (iii) the existence of a maximum and a minimum in the signal-to-noise ratio (SNR) is identifying the characteristics of the SR and stochastic reverse-resonance (SRR) phenomenon, τ and λ enhance the SR and weaken the SRR phenomenon for SNR as a function of Q, while τ (or λ) weakens (or enhances) the SR phenomenon for SNR as a function of D; and (iv) the time delay weakens the SR, and causes the SR phenomenon to disappear for SNR as a function of λ.