Synchronization of Complex Networks

Abstract

During the last decades the emergence of collective dynamics in large networks of coupled units has been investigated in many different areas of science. In particular, the effect of synchronization in systems of coupled oscillators nowadays provides a unifying framework for phenomena arising in fields such as optics, chemistry, biology and ecology (for recent reviews see [Pikovsky (2001); Boccaletti (2002); Manrubia (2004)]). Recently, complex networks have provided a challenging framework for the study of synchronization of dynamical units, based on the interplay between complexity in the overall topology and local dynamical properties of the coupled units [Strogatz (2001); Boccaletti (2006)]. This Chapter aims at reviewing the main techniques that have been proposed for assessing the propensity for synchronization (synchronizability) of a given networked system. We will describe the main applications, especially in the view of selecting the optimal topology in the coupling configuration that provides enhancement of the synchronization features.