Synchronous patterns in complex networks

Abstract

As a unique phenomenon in spatiotemporal nonlinear systems, dynamical patterns havebeen broadly interested by researchers from different fields. Recently, stimulated by therapid progress in network science, the collective behaviors of coupled oscillators in complexnetworks have received continuous interest, in which the crucial roles of network structureon dynamics have been revealed and emphasized. Despite the significance of dynamicalpatterns to the functionality of realistic systems, it remains not very clear how patterns aregenerated in complex networks. Here, from the standingpoint of cluster synchronization, wegive a brief introduction on the recent progress achieved on the formation of robust dynamicalpatterns in complex networks of coupled chaotic oscillators, including the identificationof synchronous patterns, their dynamical properties, the impact of network symmetry onpattern generation, the theoretical framework for analyzing pattern stability, and methodsfor controlling synchronous patterns. Implications of synchronous patterns to the functionalityof realistic systems will be also discussed, as well as the open questions to be addressed.