IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v199y2025ip1s0960077925006708.html

Dynamic analysis and implementation of a multi-stable Hopfield neural network

Author

Listed:
  • Li, Xuxin
  • Luo, Min
  • Zhang, Bo
  • Liu, Song

Abstract

To further investigate the influence of multistability on dynamic memory and information processing in biological neurons, this paper constructs a Hopfield neural network (HNN) model with memristive synaptic weights. The dynamical behaviors are systematically analyzed via bifurcation diagrams, Lyapunov exponent spectra, and phase portraits. The results demonstrate that the HNN not only exhibits bistability through variations in non-memristive initial values but also reveals multistability under altered memristive initial conditions, accompanied by observable transient chaotic phenomena. Furthermore, under appropriate initial conditions, the system generates infinite pairs of coexisting chaotic and periodic attractors with structural similarity and spatial offset, manifesting a symmetric multistability. Experimental validation using FPGA-based hardware implementation confirms the consistency between theoretical analysis and numerical simulations. Additionally, the application of generated chaotic sequences to image encryption is explored through numerical simulations and statistical analyses, demonstrating satisfactory encryption performance.

Suggested Citation

  • Li, Xuxin & Luo, Min & Zhang, Bo & Liu, Song, 2025. "Dynamic analysis and implementation of a multi-stable Hopfield neural network," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).
    • Handle: RePEc:eee:chsofr:v:199:y:2025:i:p1:s0960077925006708
    DOI: 10.1016/j.chaos.2025.116657
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077925006708
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2025.116657?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Wu, H.G. & Ye, Y. & Bao, B.C. & Chen, M. & Xu, Q., 2019. "Memristor initial boosting behaviors in a two-memristor-based hyperchaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 121(C), pages 178-185.
    2. Biamou, Arsene Loic Mbanda & Tamba, Victor Kamdoum & Tagne, François Kapche & Takougang, Armand Cyrille Nzeukou, 2024. "Fractional-order-induced symmetric multi-scroll chaotic attractors and double bubble bifurcations in a memristive coupled Hopfield neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    3. 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.
    4. Han Bao & Ruoyu Ding & Mengjie Hua & Huagan Wu & Bei Chen, 2022. "Initial-Condition Effects on a Two-Memristor-Based Jerk System," Mathematics, MDPI, vol. 10(3), pages 1-13, January.
    5. Zhang, Sen & Zheng, Jiahao & Wang, Xiaoping & Zeng, Zhigang, 2021. "A novel no-equilibrium HR neuron model with hidden homogeneous extreme multistability," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    6. Yu, Fei & Kong, Xinxin & Yao, Wei & Zhang, Jin & Cai, Shuo & Lin, Hairong & Jin, Jie, 2024. "Dynamics analysis, synchronization and FPGA implementation of multiscroll Hopfield neural networks with non-polynomial memristor," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    7. Zhang, Sen & Zeng, Yicheng, 2019. "A simple Jerk-like system without equilibrium: Asymmetric coexisting hidden attractors, bursting oscillation and double full Feigenbaum remerging trees," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 25-40.
    8. 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).
    Full references (including those not matched with items on IDEAS)

    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. Zhang, Jie & Yang, Liu & Zuo, Jiangang & Wei, Xiaodong & Cheng, Nana, 2025. "Design and application of spatial multi-structure hidden attractors in memristor-coupled heterogeneous neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).
    2. Yang, Ningning & Jing, Wenbo & Wu, Chaojun & Guan, XiaoMiao & Weng, CanYong, 2025. "Dynamical analysis and hardware implementation of Hopfield Neural Networks based on fractional calculus and memristor coupling," Chaos, Solitons & Fractals, Elsevier, vol. 201(P3).
    3. Yang, Liu & Zhang, Jie, 2025. "Memristor-coupled heterogeneous Hopfield neural network with switchable activation functions and its synchronization control," Chaos, Solitons & Fractals, Elsevier, vol. 200(P3).
    4. Ding, Dawei & Liu, Xiang & Zhang, Hongwei & Yang, Zongli & Jin, Fan & Chen, Siqi & Zhou, Haitao, 2025. "Reversible image encryption and hiding algorithm based on fractional-order memristive Hopfield neural network," Chaos, Solitons & Fractals, Elsevier, vol. 199(P2).
    5. Xu, Quan & Wang, Yiteng & Chen, Bei & Li, Ze & Wang, Ning, 2023. "Firing pattern in a memristive Hodgkin–Huxley circuit: Numerical simulation and analog circuit validation," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    6. Bashkirtseva, I. & Ryashko, L., 2024. "Dynamical variability, order-chaos transitions, and bursting Canards in the memristive Rulkov neuron model," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    7. Chen, Mo & Wang, Chao & Bao, Han & Ren, Xue & Bao, Bocheng & Xu, Quan, 2020. "Reconstitution for interpreting hidden dynamics with stable equilibrium point," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    8. Zizhao Xie & Jingru Sun & Yiping Tang & Xin Tang & Oluyomi Simpson & Yichuang Sun, 2023. "A K-SVD Based Compressive Sensing Method for Visual Chaotic Image Encryption," Mathematics, MDPI, vol. 11(7), pages 1-20, March.
    9. Yan, Shaohui & Wu, Xinyu & Jiang, Jiawei, 2025. "Dynamics analysis and predefined-time sliding mode synchronization of multi-scroll systems based on a single memristor model," Chaos, Solitons & Fractals, Elsevier, vol. 196(C).
    10. Wang, Ning & Xu, Dan & Li, Ze & Xu, Quan, 2023. "A general configuration for nonlinear circuit employing current-controlled nonlinearity: Application in Chua’s circuit," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    11. Ahmadi, Atefeh & Parthasarathy, Sriram & Natiq, Hayder & Jafari, Sajad & Franović, Igor & Rajagopal, Karthikeyan, 2023. "A non-autonomous mega-extreme multistable chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    12. Zhang, Shaohua & Zhang, Hongli & Wang, Cong & Lin, Hairong, 2024. "Bionic modeling and dynamics analysis of heterogeneous brain regions connected by memristive synaptic crosstalk," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    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. 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.
    15. Yamina Soula & Hadi Jahanshahi & Abdullah A. Al-Barakati & Irene Moroz, 2023. "Dynamics and Global Bifurcations in Two Symmetrically Coupled Non-Invertible Maps," Mathematics, MDPI, vol. 11(6), pages 1-13, March.
    16. Lin, Hairong & Wang, Chunhua & Du, Sichun & Yao, Wei & Sun, Yichuang, 2023. "A family of memristive multibutterfly chaotic systems with multidirectional initial-based offset boosting," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    17. Stamov, Trayan, 2024. "Practical stability criteria for discrete fractional neural networks in product form design analysis," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    18. Wan, Qiuzhen & Chen, Chaoyue & Liu, Tieqiao & Rao, Huhui & Dong, Jun, 2025. "High-dimensional memristor-coupled multiple neural networks with spatial multi-structure attractors and application in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).
    19. Sun, Shuqi & Shi, Hang & Musha, Ji'e & Yan, Dengwei & Duan, Shukai & Wang, Lidan, 2022. "Design of heterogeneous time-lags system with multi-stability and its analog circuit," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    20. Chen, Xiongjian & Wang, Ning & Wang, Yiteng & Wu, Huagan & Xu, Quan, 2023. "Memristor initial-offset boosting and its bifurcation mechanism in a memristive FitzHugh-Nagumo neuron model with hidden dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:eee:chsofr:v:199:y:2025:i:p1:s0960077925006708. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.