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Robust synchronization of memristor-based fractional-order Hopfield neural networks with parameter uncertainties

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Abstract

A new dynamic system, the fractional-order Hopfield neural networks with parameter uncertainties based on memristor are investigated in this paper. Through constructing a suitable Lyapunov function and some sufficient conditions are established to realize the robust synchronization of such system with discontinuous right-hand based on fractional-order Lyapunov direct method. Skillfully, the closure arithmetic is employed to handle the error system and the robust synchronization is achieved by analyzing the Mittag-Leffler stability. At last, two numerical examples are given to show the effectiveness of the obtained theoretical results. The first mainly shows the chaos of the system, and the other one mainly shows the results of robust synchronization.

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Acknowledgements

This work is supported by the National Nature Science Foundation of China (Nos. 11371049, 61772063) and the Fundamental Research Funds for the Central Universities (2016JBM070).

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Authors and Affiliations

  1. Department of Mathematics, Beijing Jiaotong University, Beijing, 100044, People’s Republic of China

    Shuxin Liu, Yongguang Yu & Shuo Zhang

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  1. Shuxin Liu
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  2. Yongguang Yu
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  3. Shuo Zhang
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Correspondence to Yongguang Yu.

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Liu, S., Yu, Y. & Zhang, S. Robust synchronization of memristor-based fractional-order Hopfield neural networks with parameter uncertainties. Neural Comput & Applic 31, 3533–3542 (2019). https://doi.org/10.1007/s00521-017-3274-3

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