Link exponential synchronization of discrete-time complex dynamic networks with infinite distributed delay

Er-Yong Cong; Li Zhu; Xian Zhang; Er-Yong Cong; Li Zhu; Xian Zhang

doi:10.3934/era.2026226

Electronic Research Archive

2026, Volume 34, Issue 7: 5102-5118. doi: 10.3934/era.2026226

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Link exponential synchronization of discrete-time complex dynamic networks with infinite distributed delay

Er-Yong Cong ^1,2,
Li Zhu ^{1
,
,},
Xian Zhang ^{3,4
,
,}

1.
Department of Mathematics, Harbin University, Harbin 150086, China
2.
Heilongjiang Provincial Key Laboratory of the Intelligent Perception and Intelligent Software, Harbin University, Harbin 150080, China
3.
School of Mathematical Science, Heilongjiang University, Harbin 150080, China
4.
Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems, Heilongjiang University, Harbin 150080, China

Received: 15 April 2026 Revised: 01 June 2026 Accepted: 02 June 2026 Published: 11 June 2026

This paper investigates the link exponential synchronization (LES) problem of a class of discrete-time complex dynamic networks (DTCDNs) which consist of infinite distributed delay, node complex dynamic subsystems (NCDS), and link complex dynamic subsystems (LCDS) with mutual coupling relationships. A mathematical induction method is proposed to derive the global exponential stability criterion of error systems. The obtained LES is described using linear scalar inequalities, which are very simple and easy to verify based on standard software tools such as YALMIP. Finally, it was validated through an illustrative example.
- discrete-time complex dynamic networks (DTCDNs),
- link exponential synchronization (LES),
- infinite distributed delays
Citation: Er-Yong Cong, Li Zhu, Xian Zhang. Link exponential synchronization of discrete-time complex dynamic networks with infinite distributed delay[J]. Electronic Research Archive, 2026, 34(7): 5102-5118. doi: 10.3934/era.2026226

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Abstract

This paper investigates the link exponential synchronization (LES) problem of a class of discrete-time complex dynamic networks (DTCDNs) which consist of infinite distributed delay, node complex dynamic subsystems (NCDS), and link complex dynamic subsystems (LCDS) with mutual coupling relationships. A mathematical induction method is proposed to derive the global exponential stability criterion of error systems. The obtained LES is described using linear scalar inequalities, which are very simple and easy to verify based on standard software tools such as YALMIP. Finally, it was validated through an illustrative example.

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