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 Huo; Bing Li; Yongkun Li; Nina Huo; Bing Li; Yongkun Li

doi:10.3934/math.2022202

AIMS Mathematics

2022, Volume 7, Issue 3: 3653-3679. doi: 10.3934/math.2022202

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Research article

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

1.
Key Laboratory of Applied Mathematics and Mechanism of Artificial Intelligence, Hefei University, Hefei, Anhui 230601, China
2.
School of Mathematics and Computer Science, Yunnan Minzu University, Kunming, Yunnan 650500, China
3.
School of Mathematics and Statistics, Yunnan University, Kunming, Yunnan 650091, China

Received: 18 October 2021 Accepted: 28 November 2021 Published: 06 December 2021
MSC : 34K14, 34K20, 34K50, 92B20

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.
Citation: Nina Huo, Bing Li, Yongkun Li. Global exponential stability and existence of almost periodic solutions in distribution for Clifford-valued stochastic high-order Hopfield neural networks with time-varying delays[J]. AIMS Mathematics, 2022, 7(3): 3653-3679. doi: 10.3934/math.2022202

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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.

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