两类加权哑铃网络的一致性分析  

Consensus Analysis of Two Types of Weighted Dumbbell Networks

作　　者：朱剑 李显勇 朱峰刚 高海平[4] 杨学海 鲁晓艺 ZHU Jian;LI Xianyong;ZHU Fenggang;GAO Haiping;YANG Xuehai;LU Xiaoyi(Department of Mathematics and Physics,Xinjiang Institute of Engineering,Urumqi 830023 China;School of Computer and Software Engineering,Xihua University,Chengdu 610039 China;Engineering Training Center,Xinjiang Institute of Engineering,Urumqi 830023 China;Ministry of Public Infrastructure,Xinjiang Light Industry Vocational and Technical College,Urumqi 830021 China;Department of Mechanical and Electrical Engineering,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]西华大学计算机与软件工程学院,四川成都610039 [3]新疆工程学院工程训练中心,新疆乌鲁木齐830023 [4]新疆轻工职业技术学院教务处,新疆乌鲁木齐830021 [5]新疆工程学院机电工程学院,新疆乌鲁木齐830023 [6]新疆工程学院信息工程学院,新疆乌鲁木齐830023

出　　处：《西华大学学报（自然科学版）》2024年第5期74-80,共7页Journal of Xihua University:Natural Science Edition

基　　金：国家自然科学基金(61802316);四川省科技计划资助(2022YFG0378);新疆维吾尔自治区高校基本科研业务费科研项目(XJEDU2022P129、XJEDU2024P080);国家级大学生创新创业训练项目(202310994015);新疆维吾尔自治区级大学生创新创业训练项目(S202310994033)。

摘　　要：网络的一致性是复杂网络科学的一个重要分支,其研究结果可以为理解网络的动力学行为提供理论依据。网络拓扑结构对网络一致性的鲁棒性有重要影响。文章首先根据经典的哑铃网络模型,分配边的权重,建立了符合实际应用的加权网络模型,其次结合网络一致性、图论等理论推导出加权网络的一阶和二阶一致性指标的具体解析式,进一步使用MATLAB软件数值模拟出两类哑铃网络的一致性指标对网络规模及耦合强度的依赖关系。研究结果表明,耦合强度的增大会使网络一致性增强,且节点全连接的哑铃网络具有更优的一阶与二阶一致性的鲁棒性。The consensus of networks is an important branch of complex network science,and its research results can provide the theoretical basis for understanding the dynamic behavior of networks.The network topology has a significant impact on the robustness of network consensus.This article first assigns edge weights based on the classic dumbbell network model and establishes the weighted network model that is suitable for practical applications.Secondly,the specific analytical formulas of the first-order and second-order consistency indicators of the weighted network are derived by combining the theories of network consensus and graph theory.Furthermore,MATLAB software is used to numerically simulate the dependence of the consistency indicators of two types of dumbbell networks on network size and coupling strength.Finally,it is found that the increase in coupling strength leads to the increase in network consensus,and the dumbbell network with fully connected nodes has better robustness of first-order and second-order coherence.

关 键 词：复杂网络 哑铃网络 加权 一致性 鲁棒性 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程] O157.5[自动化与计算机技术—控制科学与工程]