多层星型网络的特征值谱及同步能力分析  

Synchronizability and eigenvalues of multilayer star networks

作　　者：孙娟 李晓霞[1,2] 申玉卓 李艳雨 Sun Juan;Li Xiaoxia;Shen Yuzhuo;Li Yanyu(State Key Laboratory of Reliability ＆ Intelligence of Electrical Equipment;Key Laboratory of Electromagnetic Field ＆ Electrical Apparatus Reliability of Hebei Province,Hebei University of Technology,Tianjin 300130,China)

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

出　　处：《计算机应用研究》2018年第8期2480-2483,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：针对多层双向耦合星型网络的特征值谱对网络的同步能力进行了研究。通过严格推导出多层双向耦合星型网络特征值的解析表达式,分析了节点数、层数、层内耦合强度和层间耦合强度与网络同步能力的关系,重点分析了层数对网络同步能力的影响。网络的同步能力除了受层内耦合强度和层间叶子节点之间的耦合强度影响外,当同步域无界时,若层间叶子节点之间的耦合强度较弱,网络的同步能力还依赖于层数;当同步域有界时,网络的同步能力随节点数、层间中心节点之间的耦合强度增大而变弱;若层内耦合强度较弱,网络的同步能力随层数增大而减弱;若层间叶子节点之间的耦合强度较弱,网络的同步能力随层数增大反而增强。This paper derived strictly the spectrum of the supra-Laplace matrix of multilayer star networks through bi-directionally coupling by applying the master stability method. Through mathematical analysis of eigenvalues of the supra-Laplace matrix, this paper studied how the node number, the layer number, the intra-layer and inter-layer coupling strengths influence the synchronizability of multilayer star networks. When the synchronous domain was unbounded, the synchronizability of multilayer star networks was not only relates to the intra-layer coupling strength or the inter-layer coupling strength between the leaf nodes, but also related to the layer number. If the synchronous domain was bounded, the synchronizability of multilayer star networks was inversely proportional to the node number and the inter-layer coupling strength between the hub nodes. If the in- tralayer coupling strength was weak, the synchronizability of multilayer star networks was directly proportional to the layer number, while inversely proportional to it when the coupling strength between the leaf nodes was weak.

关 键 词：多层网络 星型网络 特征值谱 同步能力 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术]