Transition and enhancement of synchronization by time delays in stochastic Hodgkin–Huxley neuron networks

In this paper, we study the effect of time delay on spiking synchronizations in Newman–Watts networks of stochastic Hodgkin–Huxley (HH) neurons. It is found that as τ is increased, the neurons exhibit transitions from spiking synchronization (SS) to clustering anti-phase synchronization (APS) and back to SS. Furthermore, the SS after the APS is enhanced with increasing time delay. For different patch sizes (channel noise strength), network randomness (fraction of random connections), and coupling strengths, the neurons exhibit similar synchronization transitions and the APS always occurs at around τ=4, representing that the time delay-induced APS behavior is robust to the channel noise, the number of random connections, and the coupling strength. A simple explanation for this phenomenon was given in terms of the relation of spiking time-period and time delay values.Since the information processing in the neurons are fulfilled by the spiking activity of the membrane potential and the spiking synchronization plays a crucial role in the spiking activity, our results may help us understand the effect of time delay as well as the interplay of channel noise and time delay on the spiking activity and hence the information processing in stochastic neuronal systems.