多层二分耦合网络的同步性研究  

Research on Synchronization of Multi-Layer Bipartite Coupled Network

作　　者：高海平[1] 朱剑 陈星[2] 李志军[3] GAO Hai-ping;ZHU Jian;CHEN Xing;LI Zhi-jun(Ministry of Public Infrastructure,Xinjiang Light Industry Vocational and Technical College,Urumqi 830021,China;Department of Mathematics and Physics,Xinjiang Institute of Engineering,Urumqi 830023,China;Academic Affairs Ofice,Xinjiang Light Industry Vocational and Technical College,Urumqi 830021,China)

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

出　　处：《数学的实践与认识》2023年第1期175-183,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(61802316);新疆维吾尔自治区自然科学基金(2021D01A65);新疆天山英才第三期;新疆工程学院科研育人项目(2020xgy332302);新疆轻工职业技术学院校级课题项目(XJQG2022S16);国家级大学生创新创业训练项目(202110994006)。

摘　　要：多层复杂网络的同步能力分析是目前网络科学研究的热点.首先根据主稳定方程(MSF)给出多层二分耦合网络的超拉普拉斯矩阵,并得到反映其同步能力的重要指标.其次分析了二分耦合网络在同步域有界和无界的两种情况下层数、二分耦合网络节点数、层间耦合强度和层内耦合强度对同步能力的影响。最后通过数值模拟和理论实践提出控制层数、二分耦合网络节点数、层间耦合强度和层内耦合强度等参数的策略,来实现优化多层二分耦合网络的同步能力,为工程技术人员在实际应用中优化其同步能力提供有效的方案.The analysis of synchronizability of multilayer complex networks is a hot topic in network science.Firstly,the supra-Laplace matrix of multi-layer bipartite coupled network is given according to the master stability equation(MSF),and the important indexes reflecting the synchronizability of the network structure are obtained.Secondly,the effects of the number of layers,the number of nodes in the bipartite coupling network,the intra-layer and the inter-layer coupling strength on the synchronizability are analyzed under the two conditions of the bounded and unbounded synchronization domain.Finally,through numerical simulation,the strategy of controlling the parameters such as the number of layers,the number of nodes in the bipartite coupling network,the intra-layer and the inter-layer coupling strength is proposed to optimize the synchronizability of the multi-layer bipartite coupled network,which provides an effective scheme for engineers to optimize synchronizability in practical application.

关 键 词：二分耦合网络 耦合强度 数值模拟 同步性 

分 类 号：O157.5[理学—数学]