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Projective synchronization for fractional-order memristor-based neural networks with time delays

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Abstract

In this paper, the global projective synchronization for fractional-order memristor-based neural networks with multiple time delays is investigated via combining open loop control with the time-delayed feedback control. A comparison theorem for a class of fractional-order systems with multiple time delays is proposed. Based on the given comparison theorem and Lyapunov method, the synchronization conditions are derived under the framework of Filippov solution and differential inclusion theory. Several feedback control strategies are given to ensure the realization of complete synchronization, anti-synchronization and the stabilization for the fractional-order memristor-based neural networks with time delays. Finally, a numerical example is given to illustrate the effectiveness of the theoretical results.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant (No. 11371049 and No. 61772063) and the Fundamental Research Funds for the Central Universities under Grant No. 2017YJS194.

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Authors and Affiliations

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

    Yajuan Gu & Yongguang Yu

  2. School of Statistics and Mathematics, Central University of Finance and Economics, Beijing, 100081, People’s Republic of China

    Hu Wang

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  1. Yajuan Gu
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  2. Yongguang Yu
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  3. Hu Wang
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Correspondence to Yongguang Yu.

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Gu, Y., Yu, Y. & Wang, H. Projective synchronization for fractional-order memristor-based neural networks with time delays. Neural Comput & Applic 31, 6039–6054 (2019). https://doi.org/10.1007/s00521-018-3391-7

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