Synchronous patterns in complex networks

Abstract

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