Synchronization in chemically coupled neural network with input normalization

Neural dynamical synchronization is a significant phenomenon in the brain’s neural electrical activity, closely linked to various brain functions such as learning, memory, motor perception, and behavioral coordination. Previous studies have shown that neurons can readily achieve complete dynamical synchronization under linear coupling via electrical synapses, whereas achieving complete synchronization is challenging under nonlinear coupling via chemical synapses. Recent research has found that, in a specific neural network architecture (where all nodes have identical in-degrees), the network dynamics with chemical synaptic coupling can achieve complete synchronization. However, the conclusions of this study are confined to that particular network architecture and cannot be applied to general, real-world neural network structures. To address this, based on certain biological foundations, we proposed a neural network dynamical model characterized by bursting activity with normalized chemical synaptic coupling. Through theoretical analysis and numerical simulations, we discovered that this network can achieve complete synchronization if the coupling strength surpasses a particular critical threshold value. Particularly, the critical value is independent of specific network structure and solely depends on the dynamical parameter of coupling function, suggesting that there is a universal principle at play that transcends the specific architecture of the neural network. The findings in this study might provide a novel potential physiological mechanism for explaining neural network synchronization and offer a new strategy for the synchronous control of neural networks.