Matrix Projective Synchronization for a Class of Networks with Double Subsystems via the Dynamical Assistance of Incoming Links

Zhang Lili; He Yu

doi:10.12052/gdutxb.240015

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Matrix Projective Synchronization for a Class of Networks with Double Subsystems via the Dynamical Assistance of Incoming Links

更新时间：2026-05-27

- Matrix Projective Synchronization for a Class of Networks with Double Subsystems via the Dynamical Assistance of Incoming Links
- Vol. 42, Issue 2, Pages: 81-88(2025)
- 作者机构：
  
  广东工业大学数学与统计学院,广东,广州,510520
- 作者简介：
- 基金信息：
- DOI：10.12052/gdutxb.240015
  CLC： TP273
- Published：2025
- 稿件说明：
移动端阅览
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, 2025, 42(2): 81–88.

Zhang Lili, He Yu. Matrix Projective Synchronization for a Class of Networks with Double Subsystems via the Dynamical Assistance of Incoming Links[J]. 2025, 42(2): 81-88.
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, 2025, 42(2): 81–88. DOI： 10.12052/gdutxb.240015

Zhang Lili, He Yu. Matrix Projective Synchronization for a Class of Networks with Double Subsystems via the Dynamical Assistance of Incoming Links[J]. 2025, 42(2): 81-88. DOI： 10.12052/gdutxb.240015.

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。

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.

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references

NIAN X H, FU X R, CHU X Y, et al . Disturbance observer-based distributed sliding mode control of multimotor web-winding systems[J ] . IET Control Theory Applications, 2020, 14(4): 614-625.

CHU X Y, NIAN X H, XIONG H Y, et al . Robust fault estimation and fault tolerant control for three-motor web-winding systems[J ] . International Journal of Control, 2021, 94(11): 3009-3021.

HOU H, NIAN X, XU S. Decentralized guaranteed cost control with H ∞ performance for large-scale web-winding system[J ] . Asian Journal of Control, 2022, 24(1): 459-473.

ROGER D T, ANDREA B, ANDRÉ F, et al . A model of gamma-frequency network oscillations induced in the rat CA3 region by carbachol in vitro[J ] . European Journal of Neuroscience, 2000, 12(11): 4093-4106.

LI B B, WANG Y H, LI S P. Tracking control for nonlinear system with the partially available states[J]. ICIC Express Letters, 2023, 17: 741-751.

WANG Y H, WANG W L, ZHANG L L. State synchronization of controlled nodes via the dynamics of links for complex dynamical networks[J]. Neurocomputing, 2020, 384: 225-230.

GAO P T, WANG Y H, LIU L Z, et al . Asymptotical state synchronization for the controlled directed complex dynamic network via links dynamics[J ] . Neurocomputing, 2021, 448: 60-66.

CUI X K, LI H L, ZHANG L, et al . Complete synchronization for discrete-time fractional-order coupled neural networks with time delays[J ] . Chaos, Solitons and Fractals, 2023, 174: 113772.

WANG G, LU S W, LIU W B, et al . Adaptive complete synchronization of two complex networks with uncertain parameters, structures, and disturbances[J ] . Journal of Computational Science, 2021, 54: 101436.

ZHAO J X, WANG Y H, GAO P T, et al . Synchronization of complex dynamical networks with stochastic links dynamics[J ] . Entropy, 2023, 25(10): 1457.

SUN Y Q, WU H Y, CHEN Z H, et al . Outer synchronization of two different multi-links complex networks by chat tering-free control[J ] . Physica A, 2021, 584: 126354.

LI W, ZHAO L Z, SHI H J, et al . Realizing generalized outer synchronization of complex dynamical networks with stochastically adaptive coupling[J ] . Mathematics and Computers in Simulation, 2021, 187: 379-390.

ZHANG L L, LEI Y F, WANG Y H, et al . Generalized outer synchronization between non-dissipatively coupled complex networks with different-dimensional nodes[J ] . Applied Mathematical Modelling, 2018, 55: 248-161.

GUO Y R, LIU C, LIU Y H, et al . Bounded synchronization for uncertain master-slave neural networks: an adaptive impulsive control approach[J ] . Neural Networks, 2023, 162: 288-296.

GUO X F, RAO P C, LIU M. Synchronization of Kuramoto-oscillator networks based on cyber-physical system[J]. Journal of the Korean Physical Society, 2023, 82(2): 121-127.

LU B L, JIANG H J, HU C, et al . Adaptive pinning cluster synchronization of a stochastic reaction-diffusion complex network[J ] . Neural Networks, 2023, 166: 524-540.

WANG X, ZHAI S D, LUO G Q, et al . Cluster synchronization in a network of nonlinear systems with directed topology and competitive relationships[J ] . Applied Mathematics and Computation, 2022, 421: 126931.

LIN L, ZHONG J, ZHU S Y, et al . Sampled-data general partial synchronization of boolean control networks[J ] . Journal of the Franklin Institute, 2022, 359(1): 1-11.

GAO Y H, YU J, HU C, et al . Fixed/preassigned-time output synchronization for T-S fuzzy complex networks via quantized control[J ] . Nonlinear Analysis: Hybrid Systems, 2024, 51: 101434.

ZHANG L L, LEI Y F, WANG Y H, et al . Matrix projective synchronization for time-varying disturbed networks with uncertain nonlinear structures and different dimensional nodes[J ] . Neurocomputing, 2018, 311: 11-23.

ZHANG L L, WANG Y H, WANG Q Y, et al . Generalized projective synchronization for networks with one crucial node and different dimensional nodes via a single controller[J ] . Asian Journal of Control, 2020, 22(4): 1471-1483.

ZANG L L, FU X Y, WANG Y H, et al . Matrix projective synchronization for a class of discrete-time complex networks with commonality via controlling the crucial node[J ] . Neurocomputing, 2021, 461: 360-369.

GAO Z L, GUO C Y, LI Y F, et al . Stabilization of a structurally balanced complex network with similar nodes of different dimensions[J ] . Applied Mathematics and Computation, 2023, 458: 128238.

LU J Y, GUO Y P, JI Y D, et al . Finite-time synchronization for different dimensional fractional-order complex dynamical networks[J ] . Chaos, Solitons and Fractals, 2020, 130: 109433.

WU M, ZHANG L L. Finite-time partial state components synchronization control for complex dynamical networks with nonidentical nodes[J]. Journal of Guangdong University of Technology, 2023, 40(4): 94-101.

CHEN G R. A talk about systems and networks[J]. Complex Systems and Complexity Science, 2010, 7(Z1): 1-4.

GAO Z L, WANG Y H, ZHANG L L, et al . The dynamic behaviors of nodes driving the structural balance for complex dynamic networks via adaptive decentralized control[J ] . International Journal of Modem Physics B, 2018, 32(24): 1850267.

LIU S, LI K, JIANG S Y, et al . Research progress of complex network synchronization control[J ] . Journal of Technology, 2022, 22(3): 256-262.

WANG S Z, ZHANG Z Y, LIN C, et al . Fixed-time synchronization for complex-valued BAM neural networks with time-varying delays via pinning control and adaptive pinning control[J ] . Chaos, Solitons and Fractals, 2021, 153: 111583.

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