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Finite-time stability and synchronization for memristor-based fractional-order Cohen-Grossberg neural network

Author

Listed:
  • Mingwen Zheng

    (School of Science, Beijing University of Posts and Telecommunications
    School of Science, Shandong University of Technology)

  • Lixiang Li

    (Information Security Center, State Key Laboratory of Networking and Switching Technology, National Engineering Laboratory for Disaster Backup and Recovery, Beijing University of Posts and Telecommunications)

  • Haipeng Peng

    (Information Security Center, State Key Laboratory of Networking and Switching Technology, National Engineering Laboratory for Disaster Backup and Recovery, Beijing University of Posts and Telecommunications)

  • Jinghua Xiao

    (School of Science, Beijing University of Posts and Telecommunications)

  • Yixian Yang

    (Information Security Center, State Key Laboratory of Networking and Switching Technology, National Engineering Laboratory for Disaster Backup and Recovery, Beijing University of Posts and Telecommunications)

  • Hui Zhao

    (School of Science, Beijing University of Posts and Telecommunications)

Abstract

In this paper, we study the finite-time stability and synchronization problem of a class of memristor-based fractional-order Cohen-Grossberg neural network (MFCGNN) with the fractional order α ∈ (0,1 ]. We utilize the set-valued map and Filippov differential inclusion to treat MFCGNN because it has discontinuous right-hand sides. By using the definition of Caputo fractional-order derivative, the definitions of finite-time stability and synchronization, Gronwall’s inequality and linear feedback controller, two new sufficient conditions are derived to ensure the finite-time stability of our proposed MFCGNN and achieve the finite-time synchronization of drive-response systems which are constituted by MFCGNNs. Finally, two numerical simulations are presented to verify the rightness of our proposed theorems.

Suggested Citation

  • Mingwen Zheng & Lixiang Li & Haipeng Peng & Jinghua Xiao & Yixian Yang & Hui Zhao, 2016. "Finite-time stability and synchronization for memristor-based fractional-order Cohen-Grossberg neural network," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(9), pages 1-11, September.
    • Handle: RePEc:spr:eurphb:v:89:y:2016:i:9:d:10.1140_epjb_e2016-70337-6
    DOI: 10.1140/epjb/e2016-70337-6
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    Citations

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    Cited by:

    1. Du, Feifei & Lu, Jun-Guo, 2021. "New criterion for finite-time synchronization of fractional order memristor-based neural networks with time delay," Applied Mathematics and Computation, Elsevier, vol. 389(C).
    2. Pratap, A. & Raja, R. & Cao, J. & Lim, C.P. & Bagdasar, O., 2019. "Stability and pinning synchronization analysis of fractional order delayed Cohen–Grossberg neural networks with discontinuous activations," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 241-260.
    3. Boaretto, B.R.R. & Budzinski, R.C. & Prado, T.L. & Kurths, J. & Lopes, S.R., 2018. "Suppression of anomalous synchronization and nonstationary behavior of neural network under small-world topology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 126-138.
    4. Liu, Shuxin & Yu, Yongguang & Zhang, Shuo & Zhang, Yuting, 2018. "Robust stability of fractional-order memristor-based Hopfield neural networks with parameter disturbances," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 845-854.
    5. Jun Guo & Yanchao Shi & Weihua Luo & Yanzhao Cheng & Shengye Wang, 2023. "Adaptive Global Synchronization for a Class of Quaternion-Valued Cohen-Grossberg Neural Networks with Known or Unknown Parameters," Mathematics, MDPI, vol. 11(16), pages 1-16, August.
    6. Wang, Shasha & Jian, Jigui, 2023. "Predefined-time synchronization of fractional-order memristive competitive neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    7. Wang, Yang & Li, Huanyun & Guan, Yan & Chen, Mingshu, 2022. "Predefined-time chaos synchronization of memristor chaotic systems by using simplified control inputs," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).

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    Keywords

    Statistical and Nonlinear Physics;

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