Impact of Partial Time Delay on Temporal Dynamics of Watts-Strogatz Small-World Neuronal Networks

In this paper, we mainly discuss effects of partial time delay on temporal dynamics of Watts-Strogatz (WS) small-world neuronal networks by controlling two parameters. One is the time delay t and the other is the probability of partial time delay pdelay. Temporal dynamics of WS small-world neuronal networks are discussed with the aid of temporal coherence and mean firing rate. With the obtained simulation results, it is revealed that for small time delay t, the probability pdelay could weaken temporal coherence and increase mean firing rate of neuronal networks, which indicates that it could improve neuronal firings of the neuronal networks while destroying firing regularity. For large time delay t, temporal coherence and mean firing rate do not have great changes with respect to pdelay. Time delay t always has great influence on both temporal coherence and mean firing rate no matter what is the value of pdelay. Moreover, with the analysis of spike trains and histograms of interspike intervals of neurons inside neuronal networks, it is found that the effects of partial time delays on temporal coherence and mean firing rate could be the result of locking between the period of neuronal firing activities and the value of time delay t. In brief, partial time delay could have great influence on temporal dynamics of the neuronal networks.