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

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.