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Research Article | Open Access

Global exponential stability and existence of almost periodic solutions in distribution for Clifford-valued stochastic high-order Hopfield neural networks with time-varying delays

Nina Huo1Bing Li2Yongkun Li3( )
Key Laboratory of Applied Mathematics and Mechanism of Artificial Intelligence, Hefei University, Hefei, Anhui 230601, China
School of Mathematics and Computer Science, Yunnan Minzu University, Kunming, Yunnan 650500, China
School of Mathematics and Statistics, Yunnan University, Kunming, Yunnan 650091, China
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Abstract

In this paper, we consider a class of Clifford-valued stochastic high-order Hopfield neural networks with time-varying delays whose coefficients are Clifford numbers except the time delays. Based on the Banach fixed point theorem and inequality techniques, we obtain the existence and global exponential stability of almost periodic solutions in distribution of this class of neural networks. Even if the considered neural networks degenerate into real-valued, complex-valued and quaternion-valued ones, our results are new. Finally, we use a numerical example and its computer simulation to illustrate the validity and feasibility of our theoretical results.

CLC number: 34K14, 34K20, 34K50, 92B20

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AIMS Mathematics
Pages 3653-3679

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Cite this article:
Huo N, Li B, Li Y. Global exponential stability and existence of almost periodic solutions in distribution for Clifford-valued stochastic high-order Hopfield neural networks with time-varying delays. AIMS Mathematics, 2022, 7(3): 3653-3679. https://doi.org/10.3934/math.2022202

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Received: 18 October 2021
Accepted: 28 November 2021
Published: 15 March 2021
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)