Stability analysis of fractional-order quaternion-valued neural networks with multiple delays and parameter uncertainties

Guoqing Jiang; Xiaolan Liu; Lei Wang; Chongwei Zheng; Guoqing Jiang; Xiaolan Liu; Lei Wang; Chongwei Zheng

doi:10.3934/math.2025553

AIMS Mathematics

2025, Volume 10, Issue 5: 12205-12227. doi: 10.3934/math.2025553

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Research article

Stability analysis of fractional-order quaternion-valued neural networks with multiple delays and parameter uncertainties

1.
College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, Sichuan, 643000, China
2.
Key Laboratory of Higher Education of Sichuan Province for Enterprise Informationalization and Internet of Things, Zigong, Sichuan, 643000, China
3.
South Sichuan Center for Applied Mathematics, Zigong, Sichuan, 643000, China
4.
Department of Navigation, Dalian Naval Academy, Chinese People's Liberation Army, Dalian, 116000, China

Received: 01 April 2025 Revised: 10 May 2025 Accepted: 19 May 2025 Published: 27 May 2025
MSC : 34A34, 34D23, 37N25

This paper proposes a fractional-order quaternion-valued neural network (FOQVNN) model with dual proportional delays, neutral delays, and parameter uncertainties. By leveraging classical lemmas and a relaxed linear matrix inequality (LMI) condition, we prove not only the uniqueness of the equilibrium point in the proposed model, but also the global robust stability of this equilibrium. Finally, numerical simulations were provided to validate the theoretical results.
- double proportional delay,
- neutral delay,
- parameter uncertainty,
- globally robust stable,
- LMI
Citation: Guoqing Jiang, Xiaolan Liu, Lei Wang, Chongwei Zheng. Stability analysis of fractional-order quaternion-valued neural networks with multiple delays and parameter uncertainties[J]. AIMS Mathematics, 2025, 10(5): 12205-12227. doi: 10.3934/math.2025553

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Abstract

This paper proposes a fractional-order quaternion-valued neural network (FOQVNN) model with dual proportional delays, neutral delays, and parameter uncertainties. By leveraging classical lemmas and a relaxed linear matrix inequality (LMI) condition, we prove not only the uniqueness of the equilibrium point in the proposed model, but also the global robust stability of this equilibrium. Finally, numerical simulations were provided to validate the theoretical results.

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