【作者】 孙世温； 刘忠信； 陈增强； 袁著祉；

【Author】 Shiwen Sun, Zhongxin Liu, Zengqiang Chen, Zhuzhi Yuan (Department of Automation, Nankai University, Tianjin 300071, China)

【机构】 南开大学自动化系；

【摘要】 许多现实世界中的复杂系统,包括通信网络(Internet,万维网WWW)、生物系统, 交通网络等,都可以通过具有复杂拓扑结构的网络或图来描述和刻画。因此具有不同学科背景的很多研究者都致力于复杂网络这一新课题的研究。其目的是为研究网络的拓扑结构对系统性质的作用和影响。更多还原

【Abstract】 Many real-world complex systems, such as communication networks (Internet, WWW), biological systems (protein interaction networks), traffic networks and so on, can be characterized by complex networks. Thus researchers from different disciplines have put their attention on this new research topic. The main goal of the study about complex networks is to investigate how the networks’ topological characteristics affect the dynamical functions taking place on such networks. The dynamical systems of coupled oscillators have received a great deal of attention over the past two decades. Especially, recent advances in complex network research have stimulated increasing interests in understanding the relationship between the topology and synchronization phenomena in dynamical networks. In our study, we consider a system of coupled oscillators on the local-world evolving networks, which is recently proposed by Li and Chen. By varying the, parameter - local world size M, the generated networks show a transition between exponential and scale-free networks with respect to the degree distribution. The collective synchronization is investigated based on a general framework for synchronization stability of coupled oscillator systems: synchronizability of coupled oscillators can be quantified through the eigenvalues of the coupling matrix, which represents the connection topology of the system. The research emphases are laid on how the synchronization is affected by various structural properties of the underlying network. Through numerical simulations, we got the relations between synchronization and structural properties on the local world networks: as the local world size M increases, the stability of synchronization is reduces with the following changes on structural properties: the maximum node degree is raised, the heterogeneity of the degree distribution is increased, the characteristic path length is decreased, the global communication efficiency is increased, the average clustering coefficient is increased, and the maximum betweenness centrality is increased. The research results verified that that larger heterogeneity of the degree distribution, shorter characteristic path length and higher clustering do not improve synchronizability, however, in the local world networks, the increase of the maximum betweenness centrality appear to be responsible for the decrease of synchronizability.更多还原