多层单向耦合星形网络的特征值谱及同步能力分析  

Synchronizability and eigenvalues of multilayer star networks through unidirectionally coupling

作　　者：孙娟 李晓霞[1,2] 张金浩 申玉卓 李艳雨 Sun Juan Li Xiao-Xia Zhang Jin-Hao Shen Yu-Zhuo Li Yan-Yu(State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin 300130, China Key Laboratory of Electromagnetic Field and Electrical Apparatus Reliability of Hebei Province, Hebei University of Technology, Tianjin 300130, China)

机构地区：[1]省部共建电工装备可靠性与智能化国家重点实验室(河北工业大学),天津3001302 [2]河北省电磁场与电器可靠性重点实验室(河北工业大学),天津300130

出　　处：《物理学报》2017年第18期291-304,共14页Acta Physica Sinica

基　　金：河北省自然科学基金(批准号:E2011202051)资助的课题~~

摘　　要：随着复杂网络同步的进一步发展,对复杂网络的研究重点由单层网络转向更加接近实际网络的多层有向网络.本文分别严格推导出三层、多层的单向耦合星形网络的特征值谱,并分析了耦合强度、节点数、层数对网络同步能力的影响,重点分析了层数和层间中心节点之间的耦合强度对多层单向耦合星形网络同步能力的影响,得出了层数对多层网络同步能力的影响至关重要.当同步域无界时,网络的同步能力与耦合强度、层数有关,同步能力随其增大而增强;当同步域有界时,对于叶子节点向中心节点耦合的多层星形网络,当层内耦合强度较弱时,层内耦合强度的增大会使同步能力增强,而层间叶子节点之间的耦合强度、层数的增大反而会使同步能力减弱;当层间中心节点之间的耦合强度较弱时,层间中心节点之间的耦合强度、层数的增大会使同步能力增强,层内耦合强度、层间叶子节点之间的耦合强度的增大反而会使同步能力减弱.对于中心节点向叶子节点耦合的多层星形网络,层间叶子节点之间的耦合强度、层数的增大会使同步能力增强,层内耦合强度、节点数、层间中心节点之间的耦合强度的增大反而会使同步能力减弱.Previous studies on multilayer networks have found that properties of multilayer networks show great differences from those of the traditional complex networks. In this paper, we derive strictly the spectra of the Supra-Laplace matrix of three-layer star networks and multilayer star networks through unidirectionally coupling by using the master stability method to analyze the synchronizability of these two networks. Through mathematical analyses of the eigenvalues of the Supra-Laplace matrix, we explore how the node number, the intra-layer coupling strength the inter-layer coupling strength, and the layer number influence the synchronizability of multilayer star networks through unidirectionally coupling in two different ways. In particular, we focus on the layer number and the inter-layer coupling strength between the hub nodes, and then we conclude that the synchronizability of networks is greatly affected by the layer number. We find that when the synchronous region is unbounded, the synchronizability of the two different coupling multilayer star networks is related to not only the intra-layer coupling strength or the inter-layer coupling strength between the leaf nodes of the entire network, but also the layer number. If the synchronous region of two different coupling multilayer star networks is bounded, and the intra-layer coupling strength is weak, the synchronizability of the two different coupling multilayer star networks is different with the changing of the intra-layer coupling strength and the inter-layer coupling strength between the leaf nodes and the layer number. If the synchronous region of two different coupling multilayer star networks is bounded, and the inter-layer coupling strength between the hub nodes is weak, the two different coupling multilayer star networks are consistent with the changing of the intra-layer coupling strength and the layer number while different from the inter-layer coupling strength between the leaf nodes and the inter-layer coupling strength between the hub nodes. We

关 键 词：多层星形网络 有向网络 特征值谱 同步能力 

分 类 号：O157.5[理学—数学]