复杂网络上的同步斑图

Synchronous patterns in complex networks

作为非线性时空系统中特有的现象,动力学斑图受到不同研究领域人们的共同关注.近年来,受网络科学发展的影响,人们对复杂网络中的各种集体动力学行为进行了深入研究,并在此过程中认识到网络结构对网络动力学的重要影响.因时空斑图是众多复杂系统实现其功能的动力学基础,又因复杂网络结构在现实复杂系统中普遍存在,故复杂网络中的斑图行为受到人们的关注.然而,受技术和方法的限制,目前人们对复杂网络中的斑图行为研究甚少.本文以全同混沌振子组成的耦合复杂网络为例,简要介绍了近年来人们在复杂网络同步斑图研究中所取得的一些进展,包括同步斑图的动力学特征、网络对称性对同步斑图的影响、同步斑图的稳定性分析理论以及同步斑图的控制方法等.同时,文中还将围绕现实复杂网络中遇到的一些具体问题,就目前复杂网络同步斑图研究中所存在的问题和面临的挑战进行简单的讨论.

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.