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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Bibliographic Details
Published inComplexity (New York, N.Y.) Vol. 2019; no. 2019; pp. 1 - 13
Main Authors Li, Yongkun, Xiang, Jianglian
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Publishing Corporation 01.01.2019
Hindawi
Hindawi Limited
Wiley
Subjects
Algebra
Artificial neural networks
Asymptotic properties
Cellular communication
Existence theorems
Feedback control
Fixed points (mathematics)
Liapunov functions
Multiplication
Neural networks
Synchronism
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Summary: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.
ISSN:1076-2787
1099-0526
DOI:10.1155/2019/6982109