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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Yunnan University, Kunming, 650091, Yunnan, People’s Republic of China

    Yongkun Li, Jiali Qin & Bing Li

  2. School of Mathematics and Computer Science, Yunnan Nationalities University, Kunming, 650500, Yunnan, People’s Republic of China

    Bing Li

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  1. Yongkun Li
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  2. Jiali Qin
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  3. Bing Li
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Correspondence to Bing Li.

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This work is supported by the National Natural Sciences Foundation of People’s Republic of China under Grant 11361072.

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Li, Y., Qin, J. & Li, B. Anti-periodic Solutions for Quaternion-Valued High-Order Hopfield Neural Networks with Time-Varying Delays. Neural Process Lett 49, 1217–1237 (2019). https://doi.org/10.1007/s11063-018-9867-8

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