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Dynamic Behavior Analysis and Synchronization of Memristor-Coupled Heterogeneous Discrete Neural Networks

Author

Listed:
  • Minglin Ma

    (School of Automation and Electronic Information, Xiangtan University, Xiangtan 411105, China)

  • Kangling Xiong

    (School of Automation and Electronic Information, Xiangtan University, Xiangtan 411105, China)

  • Zhijun Li

    (School of Automation and Electronic Information, Xiangtan University, Xiangtan 411105, China)

  • Yichuang Sun

    (School of Engineering and Technology, University of Hertfordshire, Hatfield AL10 9AB, UK)

Abstract

Continuous memristors have been widely studied in recent years; however, there are few studies on discrete memristors in the field of neural networks. In this paper, a four-stable locally active discrete memristor (LADM) is proposed as a synapse, which is used to connect a two-dimensional Chialvo neuron and a three-dimensional KTZ neuron, and construct a simple heterogeneous discrete neural network (HDNN). Through a bifurcation diagram and Lyapunov exponents diagram, the period and chaotic regions of the discrete neural network model are shown. Through numerical analysis, it was found that the chaotic region and periodic region of the neural network based on DLAM are significantly improved. In addition, coexisting chaos and chaos attractors, coexisting periodic and chaotic attractors, and coexisting periodic and periodic attractors will appear when the initial value of the LADM is changed. Coupled by a LADM synapse, two heterogeneous discrete neurons are gradually synchronized by changing the coupling strength. This paper lays a good foundation for the future analysis of LADMs and the related research of discrete neural networks coupled by LADMs.

Suggested Citation

  • Minglin Ma & Kangling Xiong & Zhijun Li & Yichuang Sun, 2023. "Dynamic Behavior Analysis and Synchronization of Memristor-Coupled Heterogeneous Discrete Neural Networks," Mathematics, MDPI, vol. 11(2), pages 1-13, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:375-:d:1031470
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    References listed on IDEAS

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    1. Lai, Qiang & Lai, Cong & Zhang, Hui & Li, Chunbiao, 2022. "Hidden coexisting hyperchaos of new memristive neuron model and its application in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
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    3. Yuan, Fang & Xing, Guibin & Deng, Yue, 2023. "Flexible cascade and parallel operations of discrete memristor," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
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    Cited by:

    1. Chunhua Wang & Yufei Li & Gang Yang & Quanli Deng, 2025. "A Review of Fractional-Order Chaotic Systems of Memristive Neural Networks," Mathematics, MDPI, vol. 13(10), pages 1-22, May.
    2. Zhang, Shaohua & Wang, Cong & Lin, Hairong & Zhang, Hongli & Ma, Ping, 2026. "Offset-controlled plane dynamics in dual memristors-radiated discrete Hopfield neuron," Chaos, Solitons & Fractals, Elsevier, vol. 203(C).
    3. Chen, Xiongjian & Sun, Kehui & Wang, Huihai & Liu, Jin & Yao, Zhao, 2025. "Discrete neuron model based on locally active memristor: Dynamics analysis and circuit implementation," Chaos, Solitons & Fractals, Elsevier, vol. 201(P1).
    4. Yue Zhu & Chunhua Wang & Jingru Sun & Fei Yu, 2023. "A Chaotic Image Encryption Method Based on the Artificial Fish Swarms Algorithm and the DNA Coding," Mathematics, MDPI, vol. 11(3), pages 1-18, February.
    5. Othman Abdullah Almatroud & Viet-Thanh Pham & Giuseppe Grassi & Mohammad Alshammari & Sahar Albosaily & Van Van Huynh, 2023. "Design of High-Dimensional Maps with Sine Terms," Mathematics, MDPI, vol. 11(17), pages 1-10, August.
    6. Saçu, İbrahim Ethem, 2025. "Intra- and inter-layer dynamics of a two-layer Izhikevich neuron map," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).
    7. 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).
    8. Hu, Jingting & Bao, Han & Xu, Quan & Chen, Mo & Bao, Bocheng, 2024. "Synchronization generations and transitions in two map-based neurons coupled with locally active memristor," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    9. Ma, Tao & Mou, Jun & Chen, Wanzhong, 2025. "Dynamics and implementation of a functional neuron model with hyperchaotic behavior under electromagnetic radiation," Chaos, Solitons & Fractals, Elsevier, vol. 190(C).
    10. Chen, Lianyu & Muthukumar, Deivasundari & Natiq, Hayder & Mehrabbeik, Mahtab & Lei, Tengfei & Jafari, Sajad, 2025. "Relay synchronization in a multiplex memristive neuronal network with electrical and field couplings," Chaos, Solitons & Fractals, Elsevier, vol. 190(C).
    11. Hairong Lin & Chunhua Wang & Fei Yu & Jingru Sun & Sichun Du & Zekun Deng & Quanli Deng, 2023. "A Review of Chaotic Systems Based on Memristive Hopfield Neural Networks," Mathematics, MDPI, vol. 11(6), pages 1-18, March.
    12. Zhengran Cao & Chuandong Li & Man-Fai Leung, 2024. "The Synchronisation Problem of Chaotic Neural Networks Based on Saturation Impulsive Control and Intermittent Control," Mathematics, MDPI, vol. 12(1), pages 1-20, January.
    13. Wang, Chunhua & Luo, Dingwei & Deng, Quanli & Yang, Gang, 2024. "Dynamics analysis and FPGA implementation of discrete memristive cellular neural network with heterogeneous activation functions," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    14. Fei Yu & Wuxiong Zhang & Xiaoli Xiao & Wei Yao & Shuo Cai & Jin Zhang & Chunhua Wang & Yi Li, 2023. "Dynamic Analysis and FPGA Implementation of a New, Simple 5D Memristive Hyperchaotic Sprott-C System," Mathematics, MDPI, vol. 11(3), pages 1-15, January.

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