IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v189y2024ip1s0960077924011366.html

Single direction, grid and spatial multi-scroll attractors in Hopfield neural network with the variable number memristive self-connected synapses

Author

Listed:
  • Wan, Qiuzhen
  • Yang, Qiao
  • Liu, Tieqiao
  • Chen, Chaoyue
  • Shen, Kun

Abstract

Due to the synapse-like nonlinearity and memory characteristics, the memristor is often used to simulate the biological neural synapse. In this paper, a family of three-neuron Hopfield neural network (HNN) models based on the variable number memristive self-connected synapses is proposed. Firstly, a single memristive self-connected synapse (SMSCS) HNN model is constructed, which can generate a single direction multi-scroll attractor controlled by the memristor parameters. Meanwhile, its dynamic behaviors including equilibrium points, multiple coexisting attractors and controllable n-scroll chaotic attractors are analyzed. Secondly, based on the above SMSCS HNN model, two types of multiple memristive self-connected synapse (MMSCS) HNN models are constructed. By changing the control parameters of the memristors, these MMSCS HNN models can not only generate the different scroll numbers of grid and spatial multi-scroll attractors, but also can produce the spatial initial-offset coexisting attractors. The above three HNN models utilizing the variable number memristors to simulate one to three self-connected synapses can generate a class of complex chaotic attractors, which include single direction, grid and spatial multi-scroll attractors. Finally, the feasibility of the proposed HNN models is verified by the FPGA platform.

Suggested Citation

  • Wan, Qiuzhen & Yang, Qiao & Liu, Tieqiao & Chen, Chaoyue & Shen, Kun, 2024. "Single direction, grid and spatial multi-scroll attractors in Hopfield neural network with the variable number memristive self-connected synapses," Chaos, Solitons & Fractals, Elsevier, vol. 189(P1).
    • Handle: RePEc:eee:chsofr:v:189:y:2024:i:p1:s0960077924011366
    DOI: 10.1016/j.chaos.2024.115584
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924011366
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2024.115584?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. 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).
    2. Peng Yao & Huaqiang Wu & Bin Gao & Jianshi Tang & Qingtian Zhang & Wenqiang Zhang & J. Joshua Yang & He Qian, 2020. "Fully hardware-implemented memristor convolutional neural network," Nature, Nature, vol. 577(7792), pages 641-646, January.
    3. Giorgia Dellaferrera & Stanisław Woźniak & Giacomo Indiveri & Angeliki Pantazi & Evangelos Eleftheriou, 2022. "Introducing principles of synaptic integration in the optimization of deep neural networks," Nature Communications, Nature, vol. 13(1), pages 1-14, December.
    4. 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).
    5. Wan, Qiuzhen & Li, Fei & Chen, Simiao & Yang, Qiao, 2023. "Symmetric multi-scroll attractors in magnetized Hopfield neural network under pulse controlled memristor and pulse current stimulation," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    6. Lin, Hairong & Wang, Chunhua, 2020. "Influences of electromagnetic radiation distribution on chaotic dynamics of a neural network," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    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. Lai, Qiang & Qin, Minghong & Chen, Guanrong, 2025. "Neurodynamics in simple cyclic Hopfield neural network under external electromagnetic radiation and stimulating current inputs," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).
    2. Huang, Lilian & Chen, Fangyi & Geng, Feiyi & Zheng, Lei & Yu, Xihong, 2025. "Generation and control of grid multi-vortex attractors in memristive Hopfield neural network," Chaos, Solitons & Fractals, Elsevier, vol. 199(P2).
    3. Randrianantenaina, Jean Luck & Baran, Ahmet Yasin & Korkmaz, Nimet & Kiliç, Recai, 2025. "Design and FPAA simulation of multi-scroll attractors in a memristor-based Hopfield neural network," Chaos, Solitons & Fractals, Elsevier, vol. 201(P3).
    4. 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).

    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. 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).
    2. 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.
    3. Wang, Chunhua & Li, Yufei & Deng, Quanli, 2025. "Discrete-time fractional-order local active memristor-based Hopfield neural network and its FPGA implementation," Chaos, Solitons & Fractals, Elsevier, vol. 193(C).
    4. Wang, Qiao & Tian, Zean & Wu, Xianming & Li, Kunshuai & Sang, Haiwei & Yu, Xiong, 2024. "A 5D super-extreme-multistability hyperchaotic map based on parallel-cascaded memristors," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    5. 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).
    6. Lai, Qiang & Zhu, Chongkun & Qin, Minghong & Wan, Zhiqiang, 2025. "Complex dynamics and encryption application of a 3D dual-memristor oscillatory hyperchaotic map," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 236(C), pages 270-283.
    7. Lai, Qiang & Chen, Yidan, 2025. "Effect of electromagnetic radiation on double-loop neural networks and its application to image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    8. 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).
    9. Min, Fuhong & Zhang, Wen & Ji, Ziyi & Zhang, Lei, 2021. "Switching dynamics of a non-autonomous FitzHugh-Nagumo circuit with piecewise-linear flux-controlled memristor," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    10. Cheng, Guanghui & Li, Dan & Yao, Yuangen & Gui, Rong, 2023. "Multi-scroll chaotic attractors with multi-wing via oscillatory potential wells," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    11. Linfang Wang & Weizeng Li & Zhidao Zhou & Junjie An & Wang Ye & Zhi Li & Hanghang Gao & Hongyang Hu & Jing Liu & Xiaoming Chen & Ling Li & Qi Liu & Mingoo Seok & Chunmeng Dou & Ming Liu, 2025. "A near-threshold memristive computing-in-memory engine for edge intelligence," Nature Communications, Nature, vol. 16(1), pages 1-10, December.
    12. Yuzhou Xi & Yu Ning & Jie Jin & Fei Yu, 2024. "A Dynamic Hill Cipher with Arnold Scrambling Technique for Medical Images Encryption," Mathematics, MDPI, vol. 12(24), pages 1-22, December.
    13. Peng Chen & Fenghao Liu & Peng Lin & Peihong Li & Yu Xiao & Bihua Zhang & Gang Pan, 2023. "Open-loop analog programmable electrochemical memory array," Nature Communications, Nature, vol. 14(1), pages 1-9, December.
    14. Ma, Tao & Mou, Jun & Chen, Wanzhong, 2025. "Enriched dynamical behavior of a novel locally active memristor-driven neuron map," Chaos, Solitons & Fractals, Elsevier, vol. 198(C).
    15. Wang, Yanfeng & Su, Pengke & Wang, Zicheng & Sun, Junwei, 2025. "Dynamic analysis of high dimensional HNN with logistic-based memristors and application in military image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 199(P3).
    16. Ding, Xincheng & Fan, Weiwei & Wang, Ning & Su, Yuanhui & Chen, Mo & Lin, Yuan & Xu, Quan, 2025. "Dynamical behaviors and firing patterns in a fully memory-element emulator-based bionic circuit," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).
    17. Yasai Wang & Weiwei Xiong & Jianmin Yan & Yue Zhou & Chaoyi Zhu & Xiangshui Miao & Yuhui He & Yang Chai, 2026. "Brain-inspired synaptic transistors for in-situ spiking reinforcement learning with eligibility trace," Nature Communications, Nature, vol. 17(1), pages 1-10, December.
    18. Bo Tong & Tianming Du & Jinhong Du & Xin Yu & Jinmeng Tong & Jiajun Xu & Wanying Li & Zhibo Liu & Chen Li & Wencai Ren, 2026. "Multimodal ion-gated transistor based on 2D superionic conductor for in-memory computing in deep learning," Nature Communications, Nature, vol. 17(1), pages 1-11, December.
    19. Djohan Bonnet & Tifenn Hirtzlin & Atreya Majumdar & Thomas Dalgaty & Eduardo Esmanhotto & Valentina Meli & Niccolo Castellani & Simon Martin & Jean-François Nodin & Guillaume Bourgeois & Jean-Michel P, 2023. "Bringing uncertainty quantification to the extreme-edge with memristor-based Bayesian neural networks," Nature Communications, Nature, vol. 14(1), pages 1-13, December.
    20. Qin, Bo & Zhang, Ying, 2024. "Comprehensive analysis of the mechanism of sensitivity to initial conditions and fractal basins of attraction in a novel variable-distance magnetic pendulum," Chaos, Solitons & Fractals, Elsevier, vol. 183(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:189:y:2024:i:p1:s0960077924011366. 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.