基于入链动态辅助的双子系统网络的矩阵投影同步

doi:10.12052/gdutxb.240015

摘要/Abstract

摘要： 针对一类具有不同维数节点的复杂动态网络，通过设计入链动态目标和节点子系统的控制输入以实现网络的矩阵投影同步。从大系统的角度看，复杂动态网络可以视为由节点子系统和入链子系统(双子系统) 相互耦合而成。本文主要探讨由双子系统耦合而成的复杂动态网络，把节点间的入链权值作为入链子系统的状态分量，用向量微分方程分别建模节点子系统和入链子系统的动力学方程。值得指出的是，本文网络中的节点可以具有不同的状态维数。根据Lyapunov稳定性理论，通过严格的理论推导，为本文双子系统网络设计入链子系统的辅助跟踪目标，并提出节点子系统的控制策略，使得当入链子系统跟踪上辅助跟踪目标时，确保该网络实现矩阵投影同步。最后给出一个适合本文双子系统网络模型特点的具体实例，通过数值仿真展示了当入链子系统跟踪上辅助跟踪目标时，节点的矩阵投影同步误差曲线随时间推移趋于零，即该网络在入链动态辅助和对节点子系统的控制作用下已实现矩阵投影同步。这验证了本文提出的矩阵投影同步方案的有效性。

关键词: 复杂动态网络, 矩阵投影同步, 节点子系统, 入链子系统, 不同维数节点

Abstract: The matrix projective synchronization for a class of complex dynamic networks with double subsystems and different dimensional nodes is investigated and realized via designing the dynamical tracking target of incoming link subsystem and the control input of the node subsystem in this paper. From the perspective of the large system, a complex dynamical network can be regarded as a coupling system of the node subsystem and the incoming link subsystem (double subsystems) . This kind of networks with double subsystems is the investigation aim of this paper, where the incoming weight between each couple of nodes is taken as the state component of the incoming link subsystem, and the vector differential equation is used to model the dynamical equation of the node subsystem and the incoming link subsystem, respectively. It is worth pointing out that the nodes in the network can have different state dimensions. Based on the Lyapunov stability theory and via the rigorous theoretical derivation, the auxiliary tracking target of the incoming link subsystem is designed and the control strategy of the node subsystem is proposed for the network . It can be deduced that the matrix projective synchronization of our network is sure to be realized when the incoming link subsystem has tracked the auxiliary tracking target. Finally, a proper example which embodies the characteristics of our network is given. Numerical simulations illustrate that all the matrix projective synchronization error curves of nodes tend to zero as time goes to infinity when the incoming link subsystem has tracked the auxiliary tracking target. That is to say, the matrix projective synchronization of our network is achieved via the dynamical assistance of the incoming links and by the control input on the node subsystem. This verifies the validity of the matrix projective synchronization strategy proposed in this paper.

Key words: complex dynamical network, matrix projective synchronization, node subsystem, incoming link subsystem, different dimensional nodes

中图分类号:

TP273

张丽丽, 何裕. 基于入链动态辅助的双子系统网络的矩阵投影同步[J]. 广东工业大学学报,doi: 10.12052/gdutxb.240015

Zhang Li-Li, He Yu. Matrix Projective Synchronization for a Class of Networks with Double Subsystems via the Dynamical Assistance of Incoming Links[J]. Journal of Guangdong University of Technology, 2024, 41(0): 0-.doi: 10.12052/gdutxb.240015

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