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Anti-periodic Synchronization of Quaternion-valued Generalized Cellular Neural Networks with Time-varying Delays and Impulsive Effects

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  • Control Theory and Applications
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Abstract

In this paper, a class of quaternion-valued generalized cellular neural networks (QVGCNNs) with time-varying delays and impulsive effects is considered. Firstly, by constructing an appropriate Lyapunov function and applying inequality techniques, some sufficient conditions on the existence of anti-periodic solutions are established. Then, the global exponential anti-periodic synchronization of delayed QVGCNNs with impulsive effects and anti-periodic coefficients is investigated by designing a novel nonlinear state-feedback controller and constructing suitable Lyapunov functions. Our results are completely new even if the considered quaternion-valued systems degenerated into real-valued or complex-valued systems. Finally, two numerical examples are given to illustrate the feasibility and effectiveness of the obtained results.

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Authors and Affiliations

  1. Department of Mathematics, Yunnan University, Kunming, Yunnan, 650091, P. R. China

    Yongkun Li, Yanchao Fang & Jiali Qin

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  1. Yongkun Li
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  2. Yanchao Fang
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  3. Jiali Qin
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Correspondence to Yongkun Li.

Additional information

Recommended by Associate Editor Choon Ki Ahn under the direction of Editor Euntai Kim. This work is supported by The National Natural Sciences Foundation of People’s Republic of China under Grants No. 11861072 and No. 11361072. We would like to thank the anonymous referees and the editor for very helpful suggestions and comments which led to improvements of our original paper.

Yongkun Li received his Ph.D. degree in Basic Mathematics from Sichuan University in 1997. His research interests include nonlinear differential equations, dynamical systems, and neural networks.

Yanchao Fang received his M.S. degree in applied mathematics from Yunnan University in 2018. His research interests include nonlinear differential equations, dynamical systems, and neural networks.

Qiali Qin received her M.S. degree in applied mathematics from Yunnan University in 2018. Her research interests include nonlinear differential equations, dynamical systems, and neural networks.

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Li, Y., Fang, Y. & Qin, J. Anti-periodic Synchronization of Quaternion-valued Generalized Cellular Neural Networks with Time-varying Delays and Impulsive Effects. Int. J. Control Autom. Syst. 17, 1191–1208 (2019). https://doi.org/10.1007/s12555-018-0385-2

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  • DOI: https://doi.org/10.1007/s12555-018-0385-2

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