Anti-periodic Solutions for Quaternion-Valued High-Order Hopfield Neural Networks with Time-Varying Delays

Anti-periodic Solutions for Quaternion-Valued High-Order Hopfield Neural Networks with... Neural Process Lett https://doi.org/10.1007/s11063-018-9867-8 Anti-periodic Solutions for Quaternion-Valued High-Order Hopfield Neural Networks with Time-Varying Delays 1 1 1,2 Yongkun Li · Jiali Qin · Bing Li © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract In this paper, quaternion-valued high-order Hopfield neural networks (QVHHNNs) with time-varying delays are considered. Theoretically, a QVHHNN can be separated into four real-valued systems, forming an equivalent real-valued system. By using a novel con- tinuation theorem of coincidence degree theory and constructing an appropriate Lyapunov function, some sufficient conditions are derived to guarantee the existence and global expo- nential stability of anti-periodic solutions for QVHHNN, which are new and complement previously known results. Keywords High-order Hopfield neural networks · Quaternion · Coincidence degree · Anti-periodic solution · Time-vary delay 1 Introduction Quaternion, which was found by the Irish mathematician W. R. Hamilton in 1843, didn’t get much attention for quite a long time, let alone the actual applications. The skew field of quaternion is denoted by H := {q = q + iq + jq + kq }, 0 1 2 3 where q , q , q , q are real numbers and the elements i, j and k obey the http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Neural Processing Letters Springer Journals

Anti-periodic Solutions for Quaternion-Valued High-Order Hopfield Neural Networks with Time-Varying Delays

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Computer Science; Artificial Intelligence (incl. Robotics); Complex Systems; Computational Intelligence
ISSN
1370-4621
eISSN
1573-773X
D.O.I.
10.1007/s11063-018-9867-8
Publisher site
See Article on Publisher Site

Abstract

Neural Process Lett https://doi.org/10.1007/s11063-018-9867-8 Anti-periodic Solutions for Quaternion-Valued High-Order Hopfield Neural Networks with Time-Varying Delays 1 1 1,2 Yongkun Li · Jiali Qin · Bing Li © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract In this paper, quaternion-valued high-order Hopfield neural networks (QVHHNNs) with time-varying delays are considered. Theoretically, a QVHHNN can be separated into four real-valued systems, forming an equivalent real-valued system. By using a novel con- tinuation theorem of coincidence degree theory and constructing an appropriate Lyapunov function, some sufficient conditions are derived to guarantee the existence and global expo- nential stability of anti-periodic solutions for QVHHNN, which are new and complement previously known results. Keywords High-order Hopfield neural networks · Quaternion · Coincidence degree · Anti-periodic solution · Time-vary delay 1 Introduction Quaternion, which was found by the Irish mathematician W. R. Hamilton in 1843, didn’t get much attention for quite a long time, let alone the actual applications. The skew field of quaternion is denoted by H := {q = q + iq + jq + kq }, 0 1 2 3 where q , q , q , q are real numbers and the elements i, j and k obey the

Journal

Neural Processing LettersSpringer Journals

Published: Jun 1, 2018

References

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