二部组合加权网络的同步能力分析  

Synchronizability of the Bipartite Combined Weighted Networks

作　　者：裴萍[1] 卞继承[1] 朱剑 黄达[1] 高蕊 PEI Ping;BIAN Ji-cheng;ZHU Jian;HUANG Da;GAO Rui(Department of Mathematics and Physics,Xinjiang Institute of Engineering,Urumqi 830023,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》2023年第4期194-202,共9页Mathematics in Practice and Theory

基　　金：新疆维吾尔自治区自然科学基金(2021D01A65);国家级大学生创新创业训练项目(202110994006);国家级大学生创新创业训练项目(202210994014);新疆工程学院2021年度校级专项教学改革项目(2021gcxyjg28);新疆工程学院2022校级课程思政项目(2022gcxyjg26)。

摘　　要：研究了多层二部组合加权网络同步能力,首先根据主稳定函数模型(MSF)得到网络的超拉普拉斯矩阵并在同步域有界和无界两种情况下推导出反映网络同步能力的两个重要指标;其次在所得指标的基础上分析了同步能力与层数、路的节点数、完全二部图节点数、层间耦合强度和层内耦合强度之间的关系,为提高网络同步能力提供了理论依据;最后使用MATLAB软件进行了仿真图像实验,验证了理论结果的有效性.In this paper,multi-layer bipartite combined weighted networks are studied.Firstly,the supra-Laplace matrix of the corresponding multi-layer combined networks is obtained according to the master stability equation(MSF).Two important indexes reflecting the synchronizability of the networks are derived in the case of bounded and unbounded synchronization domain;Secondly,on this basis of the indexes,the relationships between the synchronizability and the number of layers,the number of nodes of the path,the nodes of the bipartite graph are analyzed,which can provide a theoretical basis for controlling the network synchronizability;finally,the simulation image experiment is carried out with MATLAB software to verify the effectiveness of the theoretical results.

关 键 词：组合网络 同步能力 完全二部图 仿真图像 

分 类 号：O157.5[理学—数学]