Impact of connection delays on noise-induced spatiotemporal patterns in neuronal networks.

In the present work, we investigate the nontrivial roles of independent Gaussian noise and time-delayed coupling on the synchronous dynamics and coherence property of Fitz Hugh-Nagumo neurons on small-world networks by numerical simulations. First, it is shown that an intermediate level of noise in the neuronal networks can optimally induce a temporal coherence state when the delay in the coupling is absent. We find that this phenomenon is robust to changes of the coupling strength and the rewiring probability of small-world networks. Then, when appropriately tuned delays with moderate values are included in the coupling, the neurons on the networks can reach higher ordered spatiotemporal patterns which are the most coherent in time and almost synchronized in space. Moreover, the tuned delays are within a range, and the period of the firing activity is delay-dependent which equals nearly to the length of the coupling delay. This result implies that the higher ordered spatiotemporal dynamics induced by intermediate delays could be the result of a locking between the period-1 neuronal spiking activity and the delay. The performance of moderate delays in enhancing the ordered spatiotemporal patterns is also examined to be robust against variations of the network randomness.