Synchronization and multistability in the coupled neurons with propagation and processing delays

The dynamics of spiking and bursting activities have attracted interest from scientists due to their significance in the brain and neural systems. In this work, the effects of processing delay, specifically the time delay in coupling, on the dynamical behaviors of the coupled Hindmarsh-Rose neurons with resting state are investigated. The results reveal that the processing delay can induce rich spiking patterns, such as anti-phase synchronous spiking, in-phase synchronous periodic bursting, anti-phase synchronous periodic bursting and anti-phase synchronous chaotic bursting, and maintained the bistability and tristability of different spiking patterns. This emphasizes that the processing delay-induced spiking patterns might not be observed in the diffusively coupled neurons with resting state with and without propagation delay. The results can help deepen the knowledge on neural synchronization and information processing in the neuronal network and brain.