Phase synchronizing in Hindmarsh–Rose neural networks with delayed chemical coupling

Although diffusive electrical connections in neuronal networks are instantaneous, excitatory/inhibitory couplings via chemical synapses encompass a transmission time-delay. In this paper neural networks with instantaneous electrical couplings and time-delayed excitatory/inhibitory chemical connections are considered and scaling of the spike phase synchronization with the unified time-delay in the network is investigated. The findings revealed that in both excitatory and inhibitory chemical connections, the phase synchronization could be enhanced by introducing time-delay. The role of the variability of the neuronal external current in the phase synchronization is also investigated. As individual neuron models, Hindmarsh–Rose model is adopted and the network structure of the electrical and chemical connections is considered to be Watts–Strogatz and directed random networks, respectively.