Graph Topology and Synchronization of Network Coupled Dynamic Systems with Time-delay
Graph Topology and Synchronization of Network Coupled Dynamic Systems with Time-delay
复制标题
时滞网络耦合动态系统的图拓扑与同步
DOI：
10.5687/iscie.19.241
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
S. Hosoe
中科院分区：
文献类型：
--
作者：
Masateru Amano;Zhiwei Luo;S. Hosoe
本文研究了由多个相同动态子系统组成的网络耦合系统的同步问题以及具有相互作用时滞的网络耦合问题。基于图论和李雅普诺夫稳定性理论，给出了网络耦合相互作用图结构下系统的全同步和轨迹有界的条件。研究结果表明，与无时滞系统不同，（1）当相互作用强度和图的边数处于某个上、下界之间时，系统会发生同步;（2）在规则图中，如完全图、星星图和圈图，当子系统总数增加时，系统的同步条件将被破坏，（3）对于小世界网络和无标度网络等复杂网络，当子系统总数增加时，同步条件比规则图更容易满足，并通过数值模拟得到了验证。
This paper studies the synchronization of network coupled systems consisting of many identical dynamic subsystems as well as network coupling with interaction time-delay. Based on graph theory and Lyapunov stability theory, the paper gives conditions for the total system synchronization and the boundedness of trajectories with respect to the graph structures of network coupling interaction. According to our study, it is revealed that, different from the systems without time-delay, (1) there will be a case where synchronization will occurs if the interaction strength and the number of the graph edges lie between some upper and lower bounds, (2) in regular graphs, such that complete-, star- and cycle graph, the synchronization conditon will be violated if total number of subsystems increases, (3) for the complex networks such as Small World Network and Scale Free Network, the synchronization conditon is more easier to be satisfied than regular graphs when the total number of subsystems increases.These are verified using numerical simulations.