Global Asymptotic Almost Periodic Synchronization of Clifford-Valued CNNs with Discrete Delays
In this paper, we are concerned with Clifford-valued cellular neural networks (CNNs) with discrete delays. Since Clifford algebra is a unital associative algebra and its multiplication is noncommutative, to overcome the difficulty of the noncommutativity of the multiplication of Clifford numbers, we...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/6982109 |
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| author | Yongkun Li Jianglian Xiang |
| author_facet | Yongkun Li Jianglian Xiang |
| author_sort | Yongkun Li |
| collection | DOAJ |
| description | In this paper, we are concerned with Clifford-valued cellular neural networks (CNNs) with discrete delays. Since Clifford algebra is a unital associative algebra and its multiplication is noncommutative, to overcome the difficulty of the noncommutativity of the multiplication of Clifford numbers, we first decompose the considered Clifford-valued neural network into 2m2n real-valued systems. Second, based on the Banach fixed point theorem, we establish the existence and uniqueness of almost periodic solutions of the considered neural networks. Then, by designing a novel state-feedback controller and constructing a proper Lyapunov function, we study the global asymptotic synchronization of the considered neural networks. Finally, a numerical example is presented to show the effectiveness and feasibility of our results. |
| format | Article |
| id | doaj-art-d5870211320b49979f3bc2ff338859c8 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-d5870211320b49979f3bc2ff338859c82025-02-03T05:57:20ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/69821096982109Global Asymptotic Almost Periodic Synchronization of Clifford-Valued CNNs with Discrete DelaysYongkun Li0Jianglian Xiang1Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, ChinaDepartment of Mathematics, Yunnan University, Kunming, Yunnan 650091, ChinaIn this paper, we are concerned with Clifford-valued cellular neural networks (CNNs) with discrete delays. Since Clifford algebra is a unital associative algebra and its multiplication is noncommutative, to overcome the difficulty of the noncommutativity of the multiplication of Clifford numbers, we first decompose the considered Clifford-valued neural network into 2m2n real-valued systems. Second, based on the Banach fixed point theorem, we establish the existence and uniqueness of almost periodic solutions of the considered neural networks. Then, by designing a novel state-feedback controller and constructing a proper Lyapunov function, we study the global asymptotic synchronization of the considered neural networks. Finally, a numerical example is presented to show the effectiveness and feasibility of our results.http://dx.doi.org/10.1155/2019/6982109 |
| spellingShingle | Yongkun Li Jianglian Xiang Global Asymptotic Almost Periodic Synchronization of Clifford-Valued CNNs with Discrete Delays Complexity |
| title | Global Asymptotic Almost Periodic Synchronization of Clifford-Valued CNNs with Discrete Delays |
| title_full | Global Asymptotic Almost Periodic Synchronization of Clifford-Valued CNNs with Discrete Delays |
| title_fullStr | Global Asymptotic Almost Periodic Synchronization of Clifford-Valued CNNs with Discrete Delays |
| title_full_unstemmed | Global Asymptotic Almost Periodic Synchronization of Clifford-Valued CNNs with Discrete Delays |
| title_short | Global Asymptotic Almost Periodic Synchronization of Clifford-Valued CNNs with Discrete Delays |
| title_sort | global asymptotic almost periodic synchronization of clifford valued cnns with discrete delays |
| url | http://dx.doi.org/10.1155/2019/6982109 |
| work_keys_str_mv | AT yongkunli globalasymptoticalmostperiodicsynchronizationofcliffordvaluedcnnswithdiscretedelays AT jianglianxiang globalasymptoticalmostperiodicsynchronizationofcliffordvaluedcnnswithdiscretedelays |