Synchronization in systems coupled via complex networks

Recently, several models of complex networks such as small world networks and scale free networks have emerged in order to model real-life networks. This paper studies the synchronization that occurs in an array of identical chaotic systems coupled via such complex networks. We show that locally coupled arrays and randomly coupled arrays form two extremes in terms of their synchronization properties. Furthermore, we show that a locally coupled array can be made to synchronize by adding arbitrarily small couplings to an arbitrarily small fraction of coupling sites. We also present a criterion to classify such complex networks according to their synchronizability in the limit.