IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i2p375-d1031470.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/2/375/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/2/375/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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).
    2. Yuan, Fang & Xing, Guibin & Deng, Yue, 2023. "Flexible cascade and parallel operations of discrete memristor," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    3. Ling Zhou & Zhenzhen You & Xiaolin Liang & Xiaowu Li, 2022. "A Memristor-Based Colpitts Oscillator Circuit," Mathematics, MDPI, vol. 10(24), pages 1-16, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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).
    4. 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).
    5. 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.
    6. 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.
    7. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Huang, Keyu & Li, Chunbiao & Cen, Xiaoliang & Chen, Guanrong, 2024. "Constructing chaotic oscillators with memory components," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    2. Mayada Abualhomos & Abderrahmane Abbes & Gharib Mousa Gharib & Abdallah Shihadeh & Maha S. Al Soudi & Ahmed Atallah Alsaraireh & Adel Ouannas, 2023. "Bifurcation, Hidden Chaos, Entropy and Control in Hénon-Based Fractional Memristor Map with Commensurate and Incommensurate Orders," Mathematics, MDPI, vol. 11(19), pages 1-19, October.
    3. Zhang, Jianlin & Bao, Han & Yu, Xihong & Chen, Bei, 2024. "Heterogeneous coexistence of extremely many attractors in adaptive synapse neuron considering memristive EMI," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    4. Peng, Yuexi & Liu, Jun & He, Shaobo & Sun, Kehui, 2023. "Discrete fracmemristor-based chaotic map by Grunwald–Letnikov difference and its circuit implementation," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    5. Ding, Dawei & Wang, Wei & Yang, Zongli & Hu, Yongbing & Wang, Jin & Wang, Mouyuan & Niu, Yan & Zhu, Haifei, 2023. "An n-dimensional modulo chaotic system with expected Lyapunov exponents and its application in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    6. Yuan, Fang & Xing, Guibin & Deng, Yue, 2023. "Flexible cascade and parallel operations of discrete memristor," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    7. Bezerra, João Inácio Moreira & Machado, Gustavo & Molter, Alexandre & Soares, Rafael Iankowski & Camargo, Vinícius, 2023. "A novel simultaneous permutation–diffusion image encryption scheme based on a discrete space map," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    8. Xu, Quan & Wang, Kai & Chen, Mo & Parastesh, Fatemeh & Wang, Ning, 2024. "Bursting and spiking activities in a Wilson neuron circuit with memristive sodium and potassium ion channels," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    9. Yao, Zhao & Sun, Kehui & Wang, Huihai, 2024. "Collective behaviors of fractional-order FithzHugh–Nagumo network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 639(C).
    10. Wu, Huagan & Bian, Yixuan & Zhang, Yunzhen & Guo, Yixuan & Xu, Quan & Chen, Mo, 2023. "Multi-stable states and synchronicity of a cellular neural network with memristive activation function," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    11. Xu, Quan & Wang, Yiteng & Wu, Huagan & Chen, Mo & Chen, Bei, 2024. "Periodic and chaotic spiking behaviors in a simplified memristive Hodgkin-Huxley circuit," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    12. Yu Liu & Yan Zhou & Biyao Guo, 2023. "Hopf Bifurcation, Periodic Solutions, and Control of a New 4D Hyperchaotic System," Mathematics, MDPI, vol. 11(12), pages 1-14, June.
    13. 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).
    14. Wang, Zhen & Ahmadi, Atefeh & Tian, Huaigu & Jafari, Sajad & Chen, Guanrong, 2023. "Lower-dimensional simple chaotic systems with spectacular features," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    15. Lin, Hairong & Wang, Chunhua & Sun, Jingru & Zhang, Xin & Sun, Yichuang & Iu, Herbert H.C., 2023. "Memristor-coupled asymmetric neural networks: Bionic modeling, chaotic dynamics analysis and encryption application," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    16. Man, Zhenlong, 2023. "Biometric information security based on double chaotic rotating diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    17. Wang, Mingxu & Fu, Xianping & Teng, Lin & Yan, Xiaopeng & Xia, Zhiqiu & Liu, Pengbo, 2024. "A new 2D-HELS hyperchaotic map and its application on image encryption using RNA operation and dynamic confusion," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    18. Lai, Qiang & Hu, Genwen & Erkan, Uǧur & Toktas, Abdurrahim, 2023. "High-efficiency medical image encryption method based on 2D Logistic-Gaussian hyperchaotic map," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    19. Ma, Tao & Mou, Jun & Banerjee, Santo & Cao, Yinghong, 2023. "Analysis of the functional behavior of fractional-order discrete neuron under electromagnetic radiation," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    20. Lai, Qiang & Yang, Liang & Liu, Yuan, 2022. "Design and realization of discrete memristive hyperchaotic map with application in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:375-:d:1031470. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.