K层层间单向耦合星形网络的同步能力分析  

Analysis of Synchronization Ability of K Unidirectional Coupled Star Networks

作　　者：朱剑 李显勇 高海平[3] ZHU Jian;LI Xianyong;GAO Haiping(Department of Mathematics and Physics,Xinjiang Institute of Engineering,Urumqi 830023 China;School of Computer and Software Engineering,Xihua University,Chengdu 610039 China;Ministry of Public Infrastructure,Xinjiang Light Industry Vocational and Technical College,Urumqi 830021 China)

机构地区：[1]新疆工程学院数理学院,新疆乌鲁木齐830023 [2]西华大学计算机与软件工程学院,四川成都610039 [3]新疆轻工职业技术学院公共基础部,新疆乌鲁木齐830021

出　　处：《西华大学学报（自然科学版）》2022年第1期59-66,共8页Journal of Xihua University:Natural Science Edition

基　　金：国家自然科学基金(61802316,61872298,61902324);新疆工程学院科研育人项目(2020xgy332302);教育部春晖计划科研合作项目(Z2015109,Z2015100);四川省教育厅基金项目(15ZA0130,16ZA0157);西华大学青年学者后备人才项目;西华大学自然科学重点基金项目(z1422615)。

摘　　要：复杂网络是网络科学的一个研究热点。复杂网络同步能力的研究重点正从单层网络同步能力转向更加接近实际网络的多层有向网络同步能力。文章基于主稳定函数方法,深入研究4层层间单向耦合星形网络的特征值谱及其同步能力,给出了4层层间单向耦合星形网络的超拉普拉斯矩阵的特征值谱;在同步域有界和无界2种情况下,分析了K层层间单向耦合星形网络的同步能力与节点数、层数、层间耦合强度、层内耦合强度和中心节点耦合强度之间的关系;最后,通过数值仿真实验,讨论了K层层间单向耦合星形网络同步能力与各参数之间的关系(K=15)。Complex network is a hot spot in network science research.With the deepening of research,the research focus of complex network is shifting from single-layer network to multi-layer directed network closer to actual network.Based on the master stability function method,the eigenvalue spectrum and synchronization ability of the four-layer unidirectional coupled star network are studied.The eigenvalue spectrum of the supra-Laplace matrix of the four-layer unidirectional coupled star network is given.The relationship between the synchronization ability of the K layer unidirectional coupled star network and the node number,the number of layers,the intra-layer coupling strength and the inter-layer coupling strength are ana-lyzed under the condition that the synchronization domain is bounded and unbounded.Finally,the simula-tion image of synchronization ability of K layer-by-layer unidirectional coupled star network is given(K=15).

关 键 词：K层星形网络 层间单向 耦合强度 同步能力 复杂网络 

分 类 号：O157.5[理学—数学] TP393.022[理学—基础数学]