Global exponential stability and existence of almost periodic solutions in distribution for Clifford-valued stochastic high-order Hopfield neural networks with time-varying delays
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 exponent...
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| Language: | English |
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AIMS Press
2022-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022202?viewType=HTML |
| _version_ | 1798021472554319872 |
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| author | Nina Huo Bing Li Yongkun Li |
| author_facet | Nina Huo Bing Li Yongkun Li |
| author_sort | Nina Huo |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T17:14:14Z |
| format | Article |
| id | doaj.art-e6a70ff6ce2c46339bef3186732cf6bc |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-11T17:14:14Z |
| publishDate | 2022-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-e6a70ff6ce2c46339bef3186732cf6bc2022-12-22T04:12:46ZengAIMS PressAIMS Mathematics2473-69882022-01-01733653367910.3934/math.2022202Global exponential stability and existence of almost periodic solutions in distribution for Clifford-valued stochastic high-order Hopfield neural networks with time-varying delaysNina Huo0Bing Li1Yongkun Li21. Key Laboratory of Applied Mathematics and Mechanism of Artificial Intelligence, Hefei University, Hefei, Anhui 230601, China2. School of Mathematics and Computer Science, Yunnan Minzu University, Kunming, Yunnan 650500, China3. School of Mathematics and Statistics, Yunnan University, Kunming, Yunnan 650091, ChinaIn 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.https://www.aimspress.com/article/doi/10.3934/math.2022202?viewType=HTMLclifford-valued neural networkstochastic neural networkhigh-order hopfield neural networkalmost periodic solution in distributionglobal exponential stability |
| spellingShingle | 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 AIMS Mathematics clifford-valued neural network stochastic neural network high-order hopfield neural network almost periodic solution in distribution global exponential stability |
| title | Global exponential stability and existence of almost periodic solutions in distribution for Clifford-valued stochastic high-order Hopfield neural networks with time-varying delays |
| title_full | Global exponential stability and existence of almost periodic solutions in distribution for Clifford-valued stochastic high-order Hopfield neural networks with time-varying delays |
| title_fullStr | Global exponential stability and existence of almost periodic solutions in distribution for Clifford-valued stochastic high-order Hopfield neural networks with time-varying delays |
| title_full_unstemmed | Global exponential stability and existence of almost periodic solutions in distribution for Clifford-valued stochastic high-order Hopfield neural networks with time-varying delays |
| title_short | Global exponential stability and existence of almost periodic solutions in distribution for Clifford-valued stochastic high-order Hopfield neural networks with time-varying delays |
| title_sort | global exponential stability and existence of almost periodic solutions in distribution for clifford valued stochastic high order hopfield neural networks with time varying delays |
| topic | clifford-valued neural network stochastic neural network high-order hopfield neural network almost periodic solution in distribution global exponential stability |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022202?viewType=HTML |
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