Existence and global exponential stability of compact almost automorphic solutions for Clifford-valued high-order Hopfield neutral neural networks with $ D $ operator

Yuwei Cao; Bing Li; Yuwei Cao; Bing Li

doi:10.3934/math.2022344

AIMS Mathematics

2022, Volume 7, Issue 4: 6182-6203. doi: 10.3934/math.2022344

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Research article

Existence and global exponential stability of compact almost automorphic solutions for Clifford-valued high-order Hopfield neutral neural networks with $ D $ operator

Yuwei Cao ,
Bing Li ^,

School of Mathematics and Computer Science, Yunnan Minzu University, Kunming, Yunnan 650500, China

Received: 13 November 2021 Revised: 31 December 2021 Accepted: 12 January 2022 Published: 18 January 2022
MSC : 34K14, 34K20, 34K40, 92B20

In this paper, a class of Clifford-valued higher-order Hopfield neural networks with $ D $ operator is studied by non-decomposition method. Except for time delays, all parameters, activation functions and external inputs of this class of neural networks are Clifford-valued functions. Based on Banach fixed point theorem and differential inequality technique, we obtain the existence, uniqueness and global exponential stability of compact almost automorphic solutions for this class of neural networks. Our results of this paper are new. In addition, two examples and their numerical simulations are given to illustrate our results.
Citation: Yuwei Cao, Bing Li. Existence and global exponential stability of compact almost automorphic solutions for Clifford-valued high-order Hopfield neutral neural networks with $ D $ operator[J]. AIMS Mathematics, 2022, 7(4): 6182-6203. doi: 10.3934/math.2022344

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Abstract

In this paper, a class of Clifford-valued higher-order Hopfield neural networks with $ D $ operator is studied by non-decomposition method. Except for time delays, all parameters, activation functions and external inputs of this class of neural networks are Clifford-valued functions. Based on Banach fixed point theorem and differential inequality technique, we obtain the existence, uniqueness and global exponential stability of compact almost automorphic solutions for this class of neural networks. Our results of this paper are new. In addition, two examples and their numerical simulations are given to illustrate our results.

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