Besicovitch almost periodic solutions to Clifford-valued high-order Hopfield fuzzy neural networks with a $ D $ operator

Bing Li; Yuan Ning; Yongkun Li; Bing Li; Yuan Ning; Yongkun Li

doi:10.3934/math.2025549

AIMS Mathematics

2025, Volume 10, Issue 5: 12104-12134. doi: 10.3934/math.2025549

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Research article

Besicovitch almost periodic solutions to Clifford-valued high-order Hopfield fuzzy neural networks with a $ D $ operator

1.
School of Mathematics and Computer Science, Yunnan Minzu University, Kunming, Yunnan 650500, China
2.
Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, China

Received: 18 January 2025 Revised: 18 April 2025 Accepted: 08 May 2025 Published: 26 May 2025
MSC : 34K14, 34K20

This paper investigated the almost periodic dynamics of a class of Clifford-valued high-order Hopfield fuzzy neural networks with time-varying delays and $ D $ operators. Based on the Banach fixed point theorem, inequality techniques, and the definition of Besicovitch almost periodicity, we obtained the existence of Besicovitch almost periodic solutions for the considered neural network. The results of this paper are novel, and the method proposed in this paper can be used to study the existence of generalized almost periodic solutions and almost automorphic solutions to high-order neural networks. Finally, we provided a numerical example and computer simulation to demonstrate the effectiveness of the results obtained in this paper.
Citation: Bing Li, Yuan Ning, Yongkun Li. Besicovitch almost periodic solutions to Clifford-valued high-order Hopfield fuzzy neural networks with a $ D $ operator[J]. AIMS Mathematics, 2025, 10(5): 12104-12134. doi: 10.3934/math.2025549

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Abstract

This paper investigated the almost periodic dynamics of a class of Clifford-valued high-order Hopfield fuzzy neural networks with time-varying delays and $ D $ operators. Based on the Banach fixed point theorem, inequality techniques, and the definition of Besicovitch almost periodicity, we obtained the existence of Besicovitch almost periodic solutions for the considered neural network. The results of this paper are novel, and the method proposed in this paper can be used to study the existence of generalized almost periodic solutions and almost automorphic solutions to high-order neural networks. Finally, we provided a numerical example and computer simulation to demonstrate the effectiveness of the results obtained in this paper.

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