两层双向加权星型网络的同步能力分析  

Research on synchronizability of two-layer bidirectional weighted star network

作　　者：李晓霞[1] 申玉卓 张金浩 孙娟 李艳雨 Li Xiaoxia;Shen Yuzhuo;Zhang Jinhao;Sun Juan;Li Yanyu(Institute of Electrical Engineering,Hebei University of Technology,Tianjin 300130,China)

机构地区：[1]河北工业大学电气工程学院,天津300130

出　　处：《计算机应用研究》2018年第11期3389-3392,共4页Application Research of Computers

基　　金：河北省自然科学基金资助项目(E2011202051)

摘　　要：对多层网络的同步性研究大多集中在无向无权的规则网络上,但是无权网络仅仅反映了不同节点之间的连通关系及网络的拓扑特征,并不能具体地描述节点间相互作用的强弱程度。针对这一问题,在两层无权星型网络的基础上,对网络中节点间的连接边进行加权,构建网络的超拉普拉斯矩阵,利用主稳定性函数法,求取该矩阵的特征值,讨论了两层双向加权星型网络的同步性在不同同步域情况下,网络各参数对同步能力的影响。同步域无界时,网络的同步能力与层间耦合强度成正比,与层内耦合强度、权重和等参数无关,与节点接收信号能力β成反比;同步域有界时,网络的同步能力与层间耦合强度、节点接收信号能力β成正比,与层内耦合强度、权重和成反比。对于双向加权网络而言,无论同步域是否有界,增强层间耦合强度,都能增强网络的同步能力。The researches on synchronization of multilayer networks are mostly concentrating on the undirected and unweighted networks.However,the unweighted network cannot describe the interaction intensity level between nodes,only to show the connectivity and topological network characteristics.Based on the two-layer unweighted star network,this paper weighted connecting edges of nodes,constructed a super-Laplace matrix network and abstracted matrix eigenvalues by the master stability method.It analyzed the impact of network parameters on the synchronizability under the two-layer bidirectional weighted star network in different synchronization regions,and then it simulated the real network preferably.In particular,when the synchronization region was unbounded,the synchronizability of the network is not only directly proportional to the inter-layer coupling strength,but also inversely proportional to the signal reception capability of the node.Whereas,it was irrelevant with the intra-layer coupling strength and the weighted sum.On the other hand,when the synchronization region was bounded,the synchronizability of the network was directly proportional to the inter-layer coupling strength and the signal reception capability of the nodes,while inversely proportional to the intra-layer coupling strength and the weighted sum.For undirected weighted networks,the increasing of the inter-layer coupling strength can enhance the synchronizability of the network both in bounded and unbounded synchronous regions.

关 键 词：加权网络 星型网络 同步性 特征值 

分 类 号：TP391[自动化与计算机技术—计算机应用技术] TP393[自动化与计算机技术—计算机科学与技术]