Skip to main content
Log in

Grid multi-double-scroll attractors in a magnetized Hopfield neural network with a memristive self-connection synapse

  • Research
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Grid multi-scroll attractors possess distinctive properties in complex topologies and functions, yet their generation mechanisms in the neural networks still need further exploration. This paper presents a novel method to generate the grid multi-double-scroll attractors within the neural networks. Firstly, a new magnetized Hopfield neural network (HNN) model under the influence of electromagnetic radiation is developed. This model utilizes an electromagnetic radiation control method based on a multi-piecewise memristor to efficiently regulate the number of single direction multi-double-scroll attractors. Secondly, the above proposed magnetized HNN model combined with a memristive self-connection synapse is constructed by using another multi-piecewise memristor to simulate the autapse of a neuron. This combined HNN model with the double multi-piecewise memristors demonstrates the grid multi-double-scroll attractors and the initial-offset behaviors. Finally, the feasibility of the proposed magnetized HNN model is verified by the FPGA platform.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Data availability

The datasets generated and/or analyzed during the current study are available from the corresponding author on a reasonable request.

References

  1. Aram, Z., Jafari, S., Ma, J., Sprott, J.C., Zendehrouh, S., Pham, V.-T.: Using chaotic artificial neural networks to model memory in the brain. Commun. Nonlinear Sci. Numer. Simul. 44, 449–459 (2017)

    Article  MathSciNet  Google Scholar 

  2. Sun, J., Wang, Y., Liu, P., Wen, S., Wang, Y.: Memristor-based neural network circuit with multimode generalization and differentiation on pavlov associative memory. IEEE Trans. Cybern. 53(5), 3351–3362 (2023)

    Article  Google Scholar 

  3. Wan, Q., Liu, J., Qin, P., Sun, K., Hong, Q.: The design of self-healing memristive network circuit based on VTA DA neurons and its application. Neurocomputing 575, 127283 (2024)

    Article  Google Scholar 

  4. Quan, X., Ding, S., Bao, H., Chen, Mo., Bao, B.: Piecewise-linear simplification for adaptive synaptic neuron model. IEEE Trans. Circuits Syst. II Express Briefs 69(3), 1832–1836 (2022)

    Google Scholar 

  5. Lai, Q., Yang, L., Chen, G.: Design and performance analysis of discrete memristive hyperchaotic systems with stuffed cube attractors and ultraboosting behaviors. IEEE Trans. Ind. Electron. 71(7), 7819–7828 (2024)

    Article  Google Scholar 

  6. Huang, L., Zhang, Y., Xiang, J., Liu, J.: Extreme multistability in a Hopfield neural network based on two biological neuronal systems. IEEE Trans. Circuits Syst. II Express Briefs 69(11), 4568–4572 (2022)

    Google Scholar 

  7. Li, X., Sun, J., Sun, Y., Wang, C., Hong, Q., Sichun, Du., Zhang, J.: Design of artificial neurons of memristive neuromorphic networks based on biological neural dynamics and structures. IEEE Trans. Circuits Syst. Regul. Pap. 71(5), 2320–2333 (2024)

    Article  Google Scholar 

  8. Li, X., Sun, J., Ma, W., Sun, Y., Wang, C., Zhang, J.: Adaptive biomimetic neuronal circuit system based on Myelin sheath function. IEEE Trans. Consum. Electron. 70(1), 3669–3679 (2024)

    Article  Google Scholar 

  9. Wan, Q., Liu, J., Liu, T., Sun, K., Qin, P.: Memristor-based circuit design of episodic memory neural network and its application in hurricane category prediction. Neural Netw. 174(6), 106268 (2024)

    Article  Google Scholar 

  10. Fei, Y., Kong, X., Yao, W., Zhang, J., Cai, S., Lin, H., Jin, J.: Dynamics analysis, synchronization and FPGA implementation of multiscroll Hopfield neural networks with non-polynomial memristor. Chaos Solitons Fractals 179, 114440 (2024)

    Article  MathSciNet  Google Scholar 

  11. Deng, Q., Wang, C., Lin, H.: Memristive Hopfield neural network dynamics with heterogeneous activation functions and its application. Chaos Solitons Fractals 178, 114387 (2024)

    Article  MathSciNet  Google Scholar 

  12. Wan, Q., Yan, Z., Li, F., Chen, S., Liu, J.: Complex dynamics in a Hopfield neural network under electromagnetic induction and electromagnetic radiation. Chaos Interdiscip. J. Nonlinear Sci. 32(7), 073107 (2022)

    Article  MathSciNet  Google Scholar 

  13. Jieyu, Lu., Xie, X., Yaping, Lu., Yalian, Wu., Li, C., Ma, M.: Dynamical behaviors in discrete memristor-coupled small-world neuronal networks. Chin. Phys. B 33(4), 048701 (2024)

    Article  Google Scholar 

  14. Ma, M., Yaping, L.: Synchronization in scale-free neural networks under electromagnetic radiation. Chaos Interdiscip. J. Nonlinear Sci. 34, 33116 (2024)

    Article  Google Scholar 

  15. Chen, C., Chen, J., Bao, H., Chen, Mo., Bao, B.: Coexisting multi-stable patterns in memristor synapse-coupled Hopfield neural network with two neurons. Nonlinear Dyn. 95, 3385–3399 (2019)

    Article  Google Scholar 

  16. Zhutao, J., Lin, Y., Chen, B., Huagan, W., Chen, M., Quan, X.: Electromagnetic radiation induced non-chaotic behaviors in a Wilson neuron model. Chin. J. Phys. 77(6), 214–222 (2022)

    MathSciNet  Google Scholar 

  17. Ding, D., Xiao, H., Yang, Z., Luo, H., Yongbing, H., Zhang, X., Liu, Y.: Coexisting multi-stability of Hopfield neural network based on coupled fractional-order locally active memristor and its application in image encryption. Nonlinear Dyn. 108(4), 4433–4458 (2022)

    Article  Google Scholar 

  18. An, X., Xiong, L., Shi, Q., Qiao, S., Zhang, L.: Dynamics explore of an improved HR neuron model under electromagnetic radiation and its applications. Nonlinear Dyn. 111(10), 9509–9535 (2023)

    Article  Google Scholar 

  19. Ding, S., Wang, N., Bao, H., Chen, B., Huagan, W., Quan, X.: Memristor synapse-coupled piecewise-linear simplified Hopfield neural network: dynamics analysis and circuit implementation. Chaos Solitons Fractals 166, 112899 (2023)

    Article  MathSciNet  Google Scholar 

  20. Tang, D., Wang, C., Lin, H., Fei, Y.: Dynamics analysis and hardware implementation of multi-scroll hyperchaotic hidden attractors based on locally active memristive hopfield neural network. Nonlinear Dyn. 112, 1511–1527 (2024)

    Article  Google Scholar 

  21. Li, C., Yang, Y., Yang, X., Zi, X., Xiao, F.: A tristable locally active memristor and its application in Hopfield neural network. Nonlinear Dyn. 108, 1697–1717 (2022)

    Article  Google Scholar 

  22. Deng, Q., Wang, C., Sun, J., Sun, Y., Jiang, J., Lin, H., Deng, Z.: Nonvolatile CMOS memristor, reconfigurable array, and its application in power load forecasting. IEEE Trans. Ind. Inf. 20(4), 6130–6141 (2024)

    Article  Google Scholar 

  23. Wang, C., Tang, D., Lin, H., Fei, Y., Sun, Y.: High-dimensional memristive neural network and its application in commercial data encryption communication. Expert Syst. Appl. 242, 122513 (2024)

    Article  Google Scholar 

  24. Doubla, I.S., Ramakrishnan, B., Njitacke, Z.T., Kengne, J., Rajagopal, K.: Hidden extreme multistability and its control with selection of a desired attractor in a non-autonomous Hopfield neuron. AEU Int. J. Electron. Commun. 144, 154059 (2022)

    Article  Google Scholar 

  25. Chen, C., Min, F., Zhang, Y., Bao, B.: Memristive electromagnetic induction effects on Hopfield neural network. Nonlinear Dyn. 106, 2559–2576 (2021)

    Article  Google Scholar 

  26. Li, Z., Zhou, H.: Regulation of firing rhythms in a four-stable memristor-based Hindmarsh–Rose neuron. Electron. Lett. 57(19), 715–717 (2021)

    Article  Google Scholar 

  27. Lai, Q., Yang, L.: Discrete memristor applied to construct neural networks with homogeneous and heterogeneous coexisting attractors. Chaos Solitons Fractals 174, 113807 (2023)

    Article  MathSciNet  Google Scholar 

  28. Zhang, S., Zheng, J.H., Wang, X., Zeng, Z.: Multi-scroll hidden attractor in memristive HR neuron model under electromagnetic radiation and its applications. Chaos Interdiscip. J. Nonlinear Sci. 31(1), 011101 (2021)

    Article  MathSciNet  Google Scholar 

  29. Fei, Y., Kong, X., Mokbel, A.A.M., Yao, W., Cai, S.: Complex dynamics, hardware implementation and image encryption application of multiscroll memeristive hopfield neural network with a novel local active memeristor. IEEE Trans. Circuits Syst. II Express Briefs 70(1), 326–330 (2023)

    Google Scholar 

  30. Wan, Q., Li, F., Chen, S., Yang, Q.: Symmetric multi-scroll attractors in magnetized Hopfield neural network under pulse controlled memristor and pulse current stimulation. Chaos Solitons Fractals 169(4), 113259 (2023)

    Article  Google Scholar 

  31. Tan, S., Sun, J., Tang, Y., Sun, Y., Wang, C.: Hyperchaotic bilateral random low-rank approximation random sequence generation method and its application on compressive ghost imaging. Nonlinear Dyn. 112, 5749–5763 (2024)

    Article  Google Scholar 

  32. Pulido-Luna, J.R., López-Rentería, J.A., Cazarez-Castro, N.R., Campos, E.: A two-directional grid multiscroll hidden attractor based on piecewise linear system and its application in pseudo-random bit generator. Integr. VLSI J. 81, 34–42 (2021)

    Article  Google Scholar 

  33. Qin, M., Lai, Q.: Expanded multi-scroll attractor system analysis and application for remote sensing image encryption. Appl. Math. Model. 125, 125–146 (2024)

    Article  MathSciNet  Google Scholar 

  34. Lai, Q., Wan, Z., Kuate, P.D.K.: Generating grid multi-scroll attractors in memristive neural networks. IEEE Trans. Circuits Syst. I Regul. Pap. 70(3), 1324–1336 (2023)

    Article  Google Scholar 

  35. Wan, Q., Chen, S., Yang, Q., Liu, J., Sun, K.: Grid multi-scroll attractors in memristive Hopfield neural network under pulse current stimulation stimulation and multi-piecewise memristor. Nonlinear Dyn. 111, 18505–18521 (2023)

    Article  Google Scholar 

  36. Lin, H., Wang, C., Xu, C., Zhang, X., Iu, H.H.C.: A memristive synapse control method to generate diversified multi-structure chaotic attractors. IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 42(3), 942–955 (2023)

    Article  Google Scholar 

  37. Silva, C.P.: Shil’nikov’s theorem-a tutorial. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 40(10), 675–682 (1993)

    Article  Google Scholar 

  38. Yu, F., Shen, H., Yu, Q., Kong, X., Sharma, P.K., Member, S., Cai, S.: Privacy protection of medical data based on multi-scroll memristive hopfield neural network. IEEE Trans. Netw. Sci. Eng. 10(2), 845–858 (2022)

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the project supported by the National Natural Science Foundation of China under Grants 61901169 and 61804037, and the Natural Science Foundation of Hunan Province under Grant 2024JJ5267.

Funding

The authors have not disclosed any funding

Author information

Authors and Affiliations

Authors

Contributions

QW: Conceptualization, validation, supervision, writing, resources, funding acquisition. SC: Investigation, methodology, data curation, writing. TL: Investigation, software, visualization. CC: Investigation, software. QY: Methodology, software.

Corresponding author

Correspondence to Qiuzhen Wan.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wan, Q., Chen, S., Liu, T. et al. Grid multi-double-scroll attractors in a magnetized Hopfield neural network with a memristive self-connection synapse. Nonlinear Dyn (2024). https://doi.org/10.1007/s11071-024-09824-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11071-024-09824-0

Keywords

Navigation