Synchronization Dynamics in Complex Networks

Previous chapters have discussed tools from graph theory and their contribution to our understanding of the structural organization of mammalian brains and its functional implications. The brain functions are mediated by complicated dynamical processes which arise from the underlying complex neural networks, and synchronization has been proposed as an important mechanism for neural information processing. In this chapter, we discuss synchronization dynamics on complex networks. We first present a general theory and tools to characterize the relationship of some structural measures of networks to their synchronizability (the ability of the networks to achieve complete synchronization) and to the organization of effective synchronization patterns on the networks. Then, we study synchronization in a realistic network of cat cortical connectivity by modeling the nodes (which are cortical areas composed of large ensembles of neurons) by a neural mass model or a subnetwork of interacting neurons. We show that if the dynamics is characterized by well-defined oscillations (neural mass model and subnetworks with strong couplings), the synchronization patterns can be understood by the general principles discussed in the first part of the chapter. With weak couplings, the model with subnetworks displays biologically plausible dynamics and the synchronization pattern reveals a hierarchically clustered organization in the network structure. Thus, the study of synchronization of complex networks can provide insights into the relationship between network topology and functional organization of complex brain networks.