Synchronization in Complex Dynamical Networks

Excitatory recurrent networks, while confirmed in theory, have not been intensely studied by simulation focused on synchronization properties. In our research, we validate on the basis of complex network models, the refinement of degree and link-level deepness, which embodies principles of topological structural nature with emphasis on the relationship between the topology and the dynamics of such complex networks. Biologically plausible excitatory networks that are maintaining this structure, develop a stable synchronized pattern of activity depending on spontaneous activity and synaptic refractoriness. We show that by fixed synaptic weights the synchronous bursts of oscillatory activity are stable and involve the whole network. As a result, by investigating conditions for synchronized oscillatory activity in several types of networks, we found that ´small world´ networks with a higher proportion of long connections can sustain a higher degree of synchronization