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Memristive bi-neuron Hopfield neural network with coexisting symmetric behaviors

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Abstract

Memristor is able to describe the electromagnetic induction evoked by membrane potential of neuron. To this end, the paper presents a simple memristive bi-neuron Hopfield neural network (MBHNN) with electromagnetic induction, where a flux-controlled memristor is used to link one neuron directionally. Coexisting symmetric behaviors are uncovered via theoretical analyses, numerical measures, and circuit simulations. By employing theoretical analyses, we demonstrate that the MBHNN model possesses symmetric solutions and symmetric equilibrium points. By utilizing numerical measures including one- and two-argument bifurcation diagrams, dynamical maps, Lyapunov exponent spectra, basins of attraction, and phase plane plots, we confirm that the proposed MBHNN model displays coexisting periodic and chaotic bubbles and coexisting symmetric attractors. In addition, based on the mathematical model, physical analog circuit is built and the corresponding PSIM circuit simulations are deployed to testify these numerically measured results.

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References

  1. J. Ma, J. Tang, Nonlinear Dyn. 89, 1569 (2017). https://doi.org/10.1007/s11071-017-3565-3

    Article  Google Scholar 

  2. P. Zhou, X. Zhang, J. Ma, Nonlinear Dyn. 108, 1681 (2022). https://doi.org/10.1007/s11071-022-07282-0

    Article  Google Scholar 

  3. I. Hussain, D. Ghosh, S. Jafari, Appl. Math. Comput. 410, 126461 (2021). https://doi.org/10.1016/j.amc.2021.126461

    Article  Google Scholar 

  4. S. Kumar, X. Wang, J.P. Strachan, Y. Yang, W.D. Lu, Nat. Rev. Mater. (2022). https://doi.org/10.1038/s41578-022-00434-z

    Article  Google Scholar 

  5. T. Deb, A.K. Ghosh, A. Mukherjee, Mat. Today Proc. 5, 2222 (2018). https://doi.org/10.1016/j.matpr.2017.09.222

    Article  Google Scholar 

  6. C.J. Hillar, N.M. Tran, J. Math. Neur. 8, 1 (2018). https://doi.org/10.1186/s13408-017-0056-2

    Article  Google Scholar 

  7. F. Parastesh, S. Jafari, H. Azarnoush, B. Hatef, H. Namazi, D. Dudkowski, Eur. Phys. J. Spec. Top. 228, 2023 (2019). https://doi.org/10.1140/epjst/e2019-800240-5

    Article  Google Scholar 

  8. Y. Pu, Z. Yi, J. Zhou, IEEE Trans. Neural Netw. Learn. Syst. 28(10), 2319 (2017). https://doi.org/10.1109/TNNLS.2016.2582512

    Article  MathSciNet  Google Scholar 

  9. F. Cai, S. Kumar, T.V. Vaerenbergh et al., Nat. Electron. 3(7), 409 (2020). https://doi.org/10.1038/s41928-020-0436-6

    Article  Google Scholar 

  10. C.J. Chen, J.Q. Chen, H. Bao, M. Chen, B.C. Bao, Nonlinear Dyn. 95, 3385 (2019). https://doi.org/10.1007/s11071-019-04762-8

    Article  Google Scholar 

  11. C.J. Chen, H. Bao, M. Chen, Q. Xu, B.C. Bao, AEÜ-Int. J Electron. Commun. 111, 152894 (2019). https://doi.org/10.1016/j.aeue.2019.152894

    Article  Google Scholar 

  12. Q. Lai, Z. Wan, H. Zhang, G. Chen, IEEE Trans. Neural Netw. Learn. Syst. (2022). https://doi.org/10.1109/TNNLS.2022.3146570

    Article  Google Scholar 

  13. V.T. Pham, S. Jafari, S. Vaidyanathan, C. Volos, X. Wang, Sci. China Technol. Sci. 59, 358 (2016). https://doi.org/10.1007/s11431-015-5981-2

    Article  ADS  Google Scholar 

  14. H. Lin, C. Wang, Y. Tan, Nonlinear Dyn. 99, 2369 (2020). https://doi.org/10.1007/s11071-019-05408-5

    Article  Google Scholar 

  15. F. Du, J.G. Lu, IEEE Trans. Neural Netw. Learn. Syst. 32(9), 3858 (2021). https://doi.org/10.1109/TNNLS.2020.3016038

    Article  MathSciNet  Google Scholar 

  16. H. Lin, C. Wang, L. Cui, Y. Sun, C. Xu, F. Yu, IEEE Trans. Ind. Informat. (2022). https://doi.org/10.1109/TII.2022.3155599

    Article  Google Scholar 

  17. F. Yu, H. Chen, X. Kong, Q. Yu, Y. Huang, S. Du, Eur. Phys. J. Plus 137, 434 (2022). https://doi.org/10.1140/epjp/s13360-022-02652-4

    Article  Google Scholar 

  18. C.J. Chen, F.H. Min, Y.Z. Zhang, B.C. Bao, Nonlinear Dyn. 106, 2559 (2021). https://doi.org/10.1007/s11071-021-06910-5

    Article  Google Scholar 

  19. H. Lin, C. Wang, Appl. Math. Comput. 369, 124840 (2020). https://doi.org/10.1016/j.amc.2019.124840

    Article  MathSciNet  Google Scholar 

  20. H. Bao, A.H. Hu, W.B. Liu, B.C. Bao, IEEE Trans. Neural Netw. Learn. Syst. 31(2), 502 (2020). https://doi.org/10.1109/TNNLS.2019.2905137

    Article  Google Scholar 

  21. B.C. Bao, A.H. Hu, H. Bao, Q. Xu, M. Chen, H.G. Wu, Complexity 2018, 3872573 (2018). https://doi.org/10.1155/2018/3872573

    Article  Google Scholar 

  22. S. Kaçar, Eur. Phys. J. Spec. Top. (2022). https://doi.org/10.1140/epjs/s11734-022-00451-7

    Article  Google Scholar 

  23. R. Li, Z. Wang, E. Dong, Nonlinear Dyn. 104, 4459 (2021). https://doi.org/10.1007/s11071-021-06574-1

    Article  Google Scholar 

  24. H. Bao, W. Liu, A. Hu, Nonlinear Dyn. 95, 43 (2019). https://doi.org/10.1007/s11071-018-4549-7

    Article  Google Scholar 

  25. Y. Xu, Y. Jia, J. Ma, A. Alsaedi, B. Ahmad, Chaos Solitons Fract. 104, 435 (2017). https://doi.org/10.1016/j.chaos.2017.09.002

    Article  ADS  Google Scholar 

  26. S. Zhang, J. Zheng, X. Wang, Z. Zeng, S. He, Nonlinear Dyn. 102, 2821 (2020). https://doi.org/10.1007/s11071-020-06072-w

    Article  Google Scholar 

  27. H. Lin, C. Wang, Q. Hong, Y. Sun, IEEE Trans. Circuits Syst. II Exp. Briefs 67(12), 3472 (2020). https://doi.org/10.1109/TCSII.2020.3000492

    Article  Google Scholar 

  28. Q. Lai, C. Lai, H. Zhang, C. Li, Chaos Solitons Fract. 158, 112017 (2022). https://doi.org/10.1016/j.chaos.2022.112017

    Article  Google Scholar 

  29. M.J. Hua, H. Bao, H.G. Wu, Q. Xu, B.C. Bao, Chin. J. Phys. 76, 217 (2022). https://doi.org/10.1016/j.cjph.2021.10.042

    Article  Google Scholar 

  30. B.C. Bao, H. Qian, Q. Xu, M. Chen, J. Wang, Y.J. Yu, Front. Comput. Neurosci. 11, 1 (2017). https://doi.org/10.3389/fncom.2017.00081

    Article  Google Scholar 

  31. I.S. Doubla, B. Ramakrishnan, Z.N. Tabekoueng, J. Kengne, K. Rajagopal, Eur. Phys. J. Spec. Top. (2022). https://doi.org/10.1140/epjs/s11734-021-00372-x

    Article  Google Scholar 

  32. T. Dong, X. Gong, T. Huang, Neural Netw. 149, 146 (2022). https://doi.org/10.1016/j.neunet.2022.02.009

    Article  Google Scholar 

  33. Q. Xu, Z. Song, H. Bao, M. Chen, B.C. Bao, AEÜ-Int. J Electron. Commun. 96, 66 (2018). https://doi.org/10.1016/j.aeue.2018.09.017

    Article  Google Scholar 

  34. J.C. Sprott, Int. J. Bifurc. Chaos 21(9), 2391 (2011). https://doi.org/10.1142/S021812741103009X

    Article  Google Scholar 

  35. M. Chen, M.X. Sun, H. Bao, Y.H. Hu, B.C. Bao, IEEE Trans. Ind. Electron. 67(3), 2197 (2020). https://doi.org/10.1109/TIE.2019.2907444

    Article  Google Scholar 

  36. H. Bao, C. Chen, Y. Hu, M. Chen, B. Bao, IEEE Trans. Circuits Syst. II Exp. Briefs 68(4), 1453 (2021). https://doi.org/10.1109/TCSII.2020.3026702

    Article  Google Scholar 

  37. A. Wolf, J.B. Swift, H.L. Swinney, J.A. Vastano, Physica D 16, 285 (1985). https://doi.org/10.1016/0167-2789(85)90011-9

    Article  ADS  MathSciNet  Google Scholar 

  38. B.C. Bao, C.J. Chen, H. Bao, X. Zhang, Q. Xu, M. Chen, Int. J. Bifurc. Chaos 29(4), 1930010 (2019). https://doi.org/10.1142/S0218127419300106

    Article  Google Scholar 

  39. L.L. Huang, Y.L. Wang, Y.C. Jiang, T.F. Lei, Math. Probl. Eng. 2021, 7457220 (2021). https://doi.org/10.1155/2021/7457220

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 61971228, 61871230), and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant No. KYCX22_1635).

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Authors and Affiliations

  1. School of Electrical and Automation Engineering, School of Computer and Electronic Information, School of Artificial Intelligence, Nanjing Normal University, Nanjing, 210023, China

    Chengjie Chen & Fuhong Min

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  1. Chengjie Chen
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The authors contribute equally to this work.

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Correspondence to Fuhong Min.

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Chen, C., Min, F. Memristive bi-neuron Hopfield neural network with coexisting symmetric behaviors. Eur. Phys. J. Plus 137, 841 (2022). https://doi.org/10.1140/epjp/s13360-022-03050-6

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