牵制控制下含不确定耦合机制的超图同步  

Hypergraph Synchronization with Uncertain Coupling Mechanism under Pinning Control

作　　者：玉婷英 石长瑶 李科赞 YU Tingying;SHI Changyao;LI Kezan(School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin Guangxi 541004,China;Center for Applied Mathematics of Guangxi(GUET),Guilin Guangxi 541004,China)

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004 [2]广西应用数学中心(桂林电子科技大学),广西桂林541004

出　　处：《广西师范大学学报（自然科学版）》2024年第2期140-151,共12页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(62166010);广西自然科学基金(2023GXNSFAA026087)。

摘　　要：超图同步是网络科学目前的热点研究问题。然而,含不确定耦合机制的超图同步研究还未见报道。为此,本文首先提出牵制控制下含不确定耦合超图的一般框架,并通过矩阵的同时块对角化技术降低误差系统的维数,为计算李雅普诺夫指数提供便利,导出含不确定耦合超图实现同步的必要条件;其次,借助李雅普诺夫稳定性理论,给出含不确定耦合超图实现同步的充分条件;最后,利用数值模拟验证理论结果的正确性。Recently,hypergraph synchronization is a hot topic in network science.However,the study of synchronization on hypergraphs with uncertain coupling mechanism is not reported.Therefore,a general framework for uncertain-coupled hypergraphs is proposed in this paper.The dimension of the error system is reduced by the simultaneous block diagonalization technique for the matrix,which facilitates the calculation of the Lyapunov exponents.On this basis,the necessary condition of synchronization of the uncertain-coupled hypergraph is obtained.Then,the sufficient condition of synchronization of the uncertain-coupled hypergraph is also obtained based on the Lyapunov stability theory.Finally,numerical simulations are conducted to verify the theoretical results.

关 键 词：同步 超图 不确定耦合 牵制控制 

分 类 号：O231[理学—运筹学与控制论]