The evolution to global burst synchronization in a modular neuronal network

In this paper, we investigated the development of global burst synchronization in a modular neuronal network at the mesoscale level. The modular network consists of some subnetworks, each of them presenting a scale-free property. Numerical results have demonstrated that, upon increasing the coupling strength, all neurons in the modular network initially burst in a desynchronous pattern; then the burst synchronization within each subnetwork is followed at the mesoscale; finally, the global burst synchronization at the macroscale is formed by the bursting activities on each subnetwork moving forward in harmony. This implies the network behavior possesses two distinct mesoscopic and macroscopic properties for some coupling strengths, i.e. the mesoscopic dynamics of burst synchronization on subnetworks is different from the macroscopic property of desynchronous activity on the whole network. It is also found that global burst synchronization can be promoted by large interconnection probability and hindered by small interconnection probability.