Journal
IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION
Volume 36, Issue 3, Pages 983-1013Publisher
OXFORD UNIV PRESS
DOI: 10.1093/imamci/dny015
Keywords
almost automorphic synchronization; quaternion-valued neural network; time delay
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Funding
- National Natural Sciences Foundation of People's Republic of China [11361072]
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In this paper, we consider the problem of the almost automorphic synchronization of quaternion-valued high-order Hopfield neural networks (QVHHNNs) with time-varying and distributed delays. Firstly, to avoid the non-commutativity of quaternion multiplication, we decompose QVHHNNs into an equivalent real-valued system. Secondly, we use the Banach fixed point theorem to obtain the existence of almost automorphic solutions of QVHHNNs. Thirdly, by designing a novel state-feedback controller and constructing suitable Lyapunov functions, we obtain that the drive-response structure of QVHHNNs with almost automorphic coefficients can realize the exponential synchronization. Our results are completely new. Finally, a numerical example is given to illustrate the feasibility of our results.
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