层间单向耦合星形圆环状网络的同步能力  

Synchronization Ability of Unidirectional Star-Ring Network Between Layers

作　　者：朱剑 高海平[2] 黄达[1] 刘乾 徐加波 ZHU Jian;GAO Hai-ping;HUANG Da;LIU Qian;XU Jia-bo(Department of Mathematics and Physics,Xinjiang Institute of Engineering,Urumqi 830023,China;Minis try of Public Infras true ture,Xinjiang Light Industry Vocational and Technical College,Urumqi 830021,China;Information Engineering College,Xinjiang Institute of Engineering,Urumqi 830023,China)

机构地区：[1]新疆工程学院数理学院,新疆乌鲁木齐830023 [2]新疆轻工职业技术学院公共基础部,新疆乌鲁木齐830021 [3]新疆工程学院信息工程学院,新疆乌鲁木齐830023

出　　处：《数学的实践与认识》2022年第7期126-134,共9页Mathematics in Practice and Theory

基　　金：新疆维吾尔自治区自然科学基金青年项目(2019D01B10);天山青年博士科技人才培养项目(2018Q074);国家自然科学基金(11661077);新疆工程学院科研育人项目(2020xgy332302);国家级大学生创新创业训练项目(202110994006)。

摘　　要：多层复杂网络同步是网络科学研究的一个前沿方向,目前对多层复杂网络同步性的研究大多集中在无向多层复杂网络上,而更加贴近于实际的多层有向网络研究很少.首先根据主稳定方程(MSF)严格计算出M层层间单向耦合星形圆环状网络的超拉普拉斯矩阵的特征值谱,并得到反映M层层间单向耦合星形圆环状网络同步能力的重要指标,其次讨论了 M层层间单向耦合星形圆环状网络在同步域为有界和无界的两种情况下同步能力与层数、节点数、层间耦合强度和层内耦合强度及中心节点耦合强度之间的关系.最后通过数值模拟给出了层间单向耦合星形圆环状网络同步能力的仿真图像,验证了理论结果的有效性.Multilayer complex network synchronization is a frontier direction of network science.At present,most of the research,on multi-layer complex network synchronization is focused on undirec ted multi-layer complex net work.But more close to the actual multi-layer directed network research is rare.The characteristic spectrum of the super-Laplace matrix of the M layer unidirectional star-ring network is studied according to the main stabilitymethod(MSF),and an important index reflecting the synchronization ability of the M layer unidirectional coupled star-ring network is obtained.Secondly,the relationship between the synchronization ability of the M layer unidirectional coupled star ring net work and the number of layers,the number of nodes,the inter-layer coupling strength and intra-layer coupling strength and the inter-layer coupling strength between the hub nodes is discussed.Finally,the simulation image of the synchronization ability of the inter-layer unidirectional coupled star ring net work is given by numerical simulation,and the validity of the theoretical results is verified.

关 键 词：星形圆环状网络 层间单向 耦合强度 同步能力 

分 类 号：O157.5[理学—数学]