Combined effects of time delay and noise on the ability of neuronal network to detect the subthreshold signal

Recently, we found that there exist several optimal noise intensities at which the subthreshold signal could be detected efficiently in small-world neuronal networks. And this phenomenon is called as multiple stochastic resonance. Based on our former obtained results, we investigate combined effects of time delay and noise on the ability of such small-world neuronal networks to detect subthreshold signal furthermore. With the numerical simulation results, we reveal three important information. Firstly, when noise intensity takes optimal values, the ability of neuronal network to detect the subthreshold signal could be either maintained at high level as delay-free case or decreased by time delay; secondly, when noise intensity is not optimal in the absence of time delay, time delay could also assist noise to detect the subthreshold signal; finally, when noise intensity reaches a certain level, the detecting ability of the neuronal network could be optimized not only at multiples of the period of the subthreshold signal but also at some small values of time delay.