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Bifurcation, chaos and fixed-time synchronization of memristor cellular neural networks

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  • Chen, Qun
  • Li, Bo
  • Yin, Wei
  • Jiang, Xiaowei
  • Chen, Xiangyong

Abstract

This study investigates a novel chaotic memristive cellular neural network (CNN) and its synchronization. Firstly, a fourth-order chaotic system with a memristor is established by introducing a CNN and a memristor model. Secondly, the dynamic behavior of the system is analyzed, including its stability, bifurcation, and chaotic attractors. In particular, Hopf bifurcations are investigated in detail. Furthermore, the effects of the memristor’s parameters and initial state on the dynamic behavior of the system are discussed. The conclusions are verified through the use of Lyapunov exponents and bifurcation diagrams. Additionally, the study examines the multistability that arises in memristive CNNs. Moreover, an analog electronic circuit is developed by creating appropriate system parameters to confirm the presence of chaotic attractors. Thirdly, fixed-time synchronization of memristor-based chaotic CNNs is achieved through the use of sliding mode control method. A stability criterion of error system is proposed, and the results are verified through simulation

Suggested Citation

  • Chen, Qun & Li, Bo & Yin, Wei & Jiang, Xiaowei & Chen, Xiangyong, 2023. "Bifurcation, chaos and fixed-time synchronization of memristor cellular neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    • Handle: RePEc:eee:chsofr:v:171:y:2023:i:c:s0960077923003417
    DOI: 10.1016/j.chaos.2023.113440
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    References listed on IDEAS

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    1. Dmitri B. Strukov & Gregory S. Snider & Duncan R. Stewart & R. Stanley Williams, 2008. "The missing memristor found," Nature, Nature, vol. 453(7191), pages 80-83, May.
    2. Yan, Jun-Juh & Yang, Yi-Sung & Chiang, Tsung-Ying & Chen, Ching-Yuan, 2007. "Robust synchronization of unified chaotic systems via sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 947-954.
    3. Xiu, Chunbo & Zhou, Ruxia & Liu, Yuxia, 2020. "New chaotic memristive cellular neural network and its application in secure communication system," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
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    Cited by:

    1. Akhmet, Marat & Tleubergenova, Madina & Zhamanshin, Akylbek, 2024. "Cohen-Grossberg neural networks with unpredictable and Poisson stable dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    2. Lai, Qiang & Yang, Liang, 2023. "Discrete memristor applied to construct neural networks with homogeneous and heterogeneous coexisting attractors," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    3. Jie Zhang & Enze Liu, 2024. "Circuit design and image encryption of CNN chaotic system based on memristor," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(7), pages 1-19, July.

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