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Global Synchronization in Finite-time of Fractional-order Complexvalued Delayed Hopfield Neural Networks

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Abstract

This paper deals with the synchronization issue of fractional-order complex-valued Hopfield neural networks with time delay. In this paper, by means of properties of the fractional-order inequality, such as Hölder inequality and Gronwall inequality, sufficient conditions are presented to guarantee the finite-time synchronization of the fractional-order complex-valued delayed neural networks when 1/2 ≤ γ < 1 and 0 < γ < 1/2. Finally, two numerical simulations are provided to show the effectiveness of the obtained results.

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Authors and Affiliations

  1. School of Electrical Engineering, Yanshan University, Qinhuangdao, 066001, China

    Xinxin Zhang, Peifeng Niu & Guoqiang Li

  2. Yanshan University, Qinhuangdao, 066001, China

    Nan Liu

Authors
  1. Xinxin Zhang
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  2. Peifeng Niu
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  3. Nan Liu
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  4. Guoqiang Li
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Corresponding author

Correspondence to Peifeng Niu.

Additional information

Recommended by Editor Jessie (Ju H.) Park. This work was jointly supported by the National Natural Science Foundation of China (61573306), the National Natural Science Foundation of China (61403331) and the Natural Science Foundation of Hebei Province of China (F2016203427). The authors are extremely grateful to anonymous reviewers for their careful reading of the manuscript and insightful comments, which help to enrich the content of the paper. We would also like to acknowledge the valuable comments and suggestions from the editors, which vastly contributed to improve the presentation of the paper.

Xinxin Zhang is working on her Ph.D. degree in the School of Electrical Engineering, Yanshan University, Qinhuangdao, China. She received the B.S. degree from Hebei Normal University of Science and Technology, Qinhuangdao, China, in 2013. She received the master’s degree from Yanshan University, Qinhuangdao, China, in 2016. Her current research interests include fractional-order neural networks.

Peifeng Niu received his Ph.D. degree from Dongbei University in 1997. He is currently working in the School of Electrical Engineering, Yanshan University, Qinhuangdao, China. His research interests include thermal process automation, metallurgical automation, artificial intelligence control, machine learning and neural network.

Nan Liu has received her College degree, and she is currently working in the Yanshan University, Qinhuangdao, China. Her research interest includes computer technology.

Guoqiang Li received his Ph.D. degree form Yanshan Univer- sity, Qinhuangdao, China. He is currently working in the School of Electrical Engineering, Yanshan University, Qinhuangdao, China. His research interests include artificial intelligent, machine learning and the modeling and control of complex industrial systems.

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Zhang, X., Niu, P., Liu, N. et al. Global Synchronization in Finite-time of Fractional-order Complexvalued Delayed Hopfield Neural Networks. Int. J. Control Autom. Syst. 17, 521–535 (2019). https://doi.org/10.1007/s12555-018-0167-x

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  • DOI: https://doi.org/10.1007/s12555-018-0167-x

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