Cluster synchronization and firing rate oscillation induced by time delay in random network of adaptive exponential integrate-and-fire neural system

Both time delay and coupling form are the most important factors in neural networks. The properties of firing rate oscillation and cluster synchronization induced by time delay are studied in random network of different coupling neurons. In previous work, the firing rate oscillation of cortical network was observed at the presence of three factors (time delay, weak sinusoidal signal, and noise). Here, we found that the firing rate oscillation can be induced only by the time delay, and the spike train can be propagated at a certain interval time, which is consistent with the value of delay time. Furthermore, the phenomenon of cluster synchronization occurs in random network, which may originates from network structure, and this connection between the neurons trigger spikes within a time-restricted window, resulting in cluster synchronization between corresponding neurons. These numerical results provide a potential theoretical basis for certain pathological brain rhythms associated with epileptic seizures. Graphical abstract