Synchronization of networks

Abstract

We study the synchronization of coupled dynamical systems on networks. The dynamics is governed by a local nonlinear oscillator for each node of the network; interactions connecting different nodes via the links of the network. We consider existence; stability conditions for both single- multi-cluster synchronization. For networks with time-varying topology we compare the synchronization properties of these networks with the corresponding time-average network. We find that if the different coupling matrices corresponding to the time-varying networks commute with each other then the stability of the synchronized state for both the time-varying; the time-average topologies are approximately the same. On the other hand; for non-commuting coupling matrices the stability of the synchronized state for the time-varying topology is in general better than the time-average topology.