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

  • Yongkun Li
  • Jiali Qin
  • Bing Li
Article

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 continuation theorem of coincidence degree theory and constructing an appropriate Lyapunov function, some sufficient conditions are derived to guarantee the existence and global exponential 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 

Notes

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsYunnan UniversityKunmingPeople’s Republic of China
  2. 2.School of Mathematics and Computer ScienceYunnan Nationalities UniversityKunmingPeople’s Republic of China

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