Effects of partial time delay on detecting subthreshold signal in Newman–Watts neuronal networks

Information transition delay is an inherent factor in neuronal systems and has great influences on their dynamical behaviors. For theoretical studies about time delay in neuronal systems, researchers usually set all connections between neurons to be delayed. However, in real neural systems, communication between some connected neurons maybe instantaneous which make the connection be delay-free. Thus, we will discuss effects of partial time delay on detecting subthreshold signal of neuronal systems in this paper from the viewpoint of stochastic resonance. Partial time delay is introduced by assuming that time delay between two connected neurons to be τ (which is not zero) with a probability pdelay. With the obtained numerical results, we show that the ability of detecting subthreshold signal could be reduced or enhanced strongly depending on the values of pdelay and τ. Especially, the detecting ability could be enhanced by a wide range of time delay τ when pdelay is small. It means that partial time delay could have quite different influences on the ability of detecting subthreshold signal as comparing with the full time delay case (all connections are delayed). Meanwhile, we also exhibit that network topology, noise intensity and coupling strength could have great influences on the effects of partial time delay on detecting subthreshold signal of the neuronal systems.