Global exponential synchronization of discrete-time high-order BAM neural networks with multiple time-varying delays

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

doi:10.3934/math.20241605

AIMS Mathematics

2024, Volume 9, Issue 12: 33632-33648. doi: 10.3934/math.20241605

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Research article

Global exponential synchronization of discrete-time high-order BAM neural networks with multiple time-varying delays

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: 16 October 2024 Revised: 11 November 2024 Accepted: 22 November 2024 Published: 27 November 2024
MSC : 93D20

The global exponential synchronization (GES) problem of a class of discrete-time high-order bidirectional associative memory neural networks (BAMNNs) with multiple time-varying delays (T-VDs) is studied. We investigate novel delay-dependent global exponential stability criteria for the error system by proposing a mathematical induction method. The global exponential stability criteria that have been obtained are described through linear scalar inequalities. These exponential synchronization conditions are very simple and convenient for verification based on standard software tools (such as YALMIP). Lastly, an instance is presented to demonstrate the validity of the theoretical findings.
- discrete-time high-order BAM neural network,
- multiple time-varying delays,
- global exponential synchronization,
- linear scalar inequalities,
- controller gains
Citation: Er-yong Cong, Li Zhu, Xian Zhang. Global exponential synchronization of discrete-time high-order BAM neural networks with multiple time-varying delays[J]. AIMS Mathematics, 2024, 9(12): 33632-33648. doi: 10.3934/math.20241605

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Abstract

The global exponential synchronization (GES) problem of a class of discrete-time high-order bidirectional associative memory neural networks (BAMNNs) with multiple time-varying delays (T-VDs) is studied. We investigate novel delay-dependent global exponential stability criteria for the error system by proposing a mathematical induction method. The global exponential stability criteria that have been obtained are described through linear scalar inequalities. These exponential synchronization conditions are very simple and convenient for verification based on standard software tools (such as YALMIP). Lastly, an instance is presented to demonstrate the validity of the theoretical findings.

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