Global exponential stability conditions for quaternion-valued neural networks with leakage, transmission and distribution delays

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

doi:10.3934/math.2023970

AIMS Mathematics

2023, Volume 8, Issue 8: 19018-19038. doi: 10.3934/math.2023970

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Research article

Global exponential stability conditions for quaternion-valued neural networks with leakage, transmission and distribution delays

Li Zhu ¹,
Er-yong Cong ^{1,2
,
,},
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: 05 April 2023 Revised: 16 May 2023 Accepted: 25 May 2023 Published: 06 June 2023
MSC : 93D20

This paper studies the global exponential stability problem of quaternion-valued neural networks (QVNNs) with leakage, transmission, and distribution delays. To address this issue, a direct method based on system solutions is proposed to ensure the global exponential stability of the considered network models. In addition, this method does not need to construct any Lyapunov-Krasovskii functional, which greatly reduces the amount of computation. Finally, a numerical example is given to demonstrate the effectiveness of the proposed results.
- global exponential stability,
- distribution delays,
- transmission time-varying delays,
- quaternion-valued neural networks,
- leakage delay
Citation: Li Zhu, Er-yong Cong, Xian Zhang. Global exponential stability conditions for quaternion-valued neural networks with leakage, transmission and distribution delays[J]. AIMS Mathematics, 2023, 8(8): 19018-19038. doi: 10.3934/math.2023970

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Abstract

This paper studies the global exponential stability problem of quaternion-valued neural networks (QVNNs) with leakage, transmission, and distribution delays. To address this issue, a direct method based on system solutions is proposed to ensure the global exponential stability of the considered network models. In addition, this method does not need to construct any Lyapunov-Krasovskii functional, which greatly reduces the amount of computation. Finally, a numerical example is given to demonstrate the effectiveness of the proposed results.

References

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