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Dynamical analysis in dual-memristor-based FitzHugh–Nagumo circuit and its coupling finite-time synchronization

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Abstract

This paper presents an improved dual-memristor-based FitzHugh–Nagumo (DM-FHN) system, which is a non-autonomous circuit derived from FitzHugh–Nagumo (FHN) neuron circuit by substituting the tunnel diode with hyperbolic tangent memductance and connecting an active charge-controlled memristor in series with an inductor. The analysis model of the system is established first, and the rich dynamic behaviors of the system, varying with the circuit component parameters, are studied via the phase diagram, bifurcation diagram and Lyapunov exponential spectrum. Some interesting phenomena, such as bifurcation, periodic-chaotic state transition, periodic-chaotic bubbles, multistability phenomenon, and symmetrical behaviors, are observed. The finite-time synchronization of two coupled DM-FHN neurons for different behaviors due to different initial conditions is also studied. The cubic flux-controlled memristor is used as a synapse between the coupling circuits. The sufficient synchronization conditions for the unidirectional and bidirectional coupling DM-FHN circuits are derived respectively and the influence of the system initial values on the coupling synchronization is also investigated. The rich synchronous dynamics of the coupled DM-FHN systems are illustrated by the numerical simulations, the result of which also validates the presented analysis model.

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My manuscript has associated data in a data repository.

References

  1. L.O. Chua, Int. J. Remote Sens. 18, 507–519 (1971)

    Google Scholar 

  2. D.B. Strukov, G.S. Snider, D.R. Stewart et al., Nature 453, 80–83 (2008)

    Article  ADS  Google Scholar 

  3. K. Viktoria, K. Vassilia, Int. J. Remote Sens. 41, 4102–4135 (2020)

    Article  Google Scholar 

  4. S. Kumar, J.P. Strachan, R.S. Williams, Nature 548, 318–321 (2017)

    Article  ADS  Google Scholar 

  5. Z.R. Wang, S. Joshi, S.E. Savel’ev, Nat. Mater. 16, 101–108 (2017)

    Article  ADS  Google Scholar 

  6. C.H. Wang, H.R. Lin, J.G. Sun et al., J. Electron. Inf. Technol. 42, 795–810 (2020)

    Google Scholar 

  7. Y.G. Yu, M. Shi, H.Y. Kang et al., Nonlinear Dyn. 100, 891–906 (2020)

    Article  Google Scholar 

  8. H.B. Bao, J.H. Park, J.D. Cao, IEEE Trans. Neural Netw. Learn. Syst. 27, 190–201 (2016)

    Article  MathSciNet  Google Scholar 

  9. R. Fitzhugh, Biophys. J. 1, 445–466 (1961)

    Article  ADS  Google Scholar 

  10. J. Nagumo, S. Arimoto, S. Yoshizawa, Proc. Ire. 50, 2061–2070 (1962)

    Article  Google Scholar 

  11. J.H. Zhang, X.F. Liao, A.E.Ü. Int, J. Electron. Commun. 75, 82–90 (2017)

    Article  Google Scholar 

  12. J.H. Zhang, X.F. Liao, Nonlinear Dyn. 95, 1269–1282 (2019)

    Article  Google Scholar 

  13. H. Bao, W.B. Liu, M. Chen, Nonlinear Dyn. 96, 1879–1894 (2019)

    Article  Google Scholar 

  14. M. Chen, J.W. Qi, Q. Xu et al., AEÜ Int. J. Electron. Commun. 201940, 152840 (2019)

    Article  Google Scholar 

  15. M. Chen, J.W. Qi, H.G. Wu et al., Sci. China Technol. Sci. 63, 1035–1044 (2020)

    Article  ADS  Google Scholar 

  16. W. Yan, C.H. Wang, Y.H. Sun et al., Neurocomputing 404, 367–380 (2020)

    Article  Google Scholar 

  17. A.L. Shanmugam, P. Mani, R. Rajan et al., IEEE Trans. Cybern. 50, 911–922 (2020)

    Article  Google Scholar 

  18. W.P. Wang, J. Xiao, X. Luo et al., Chaos Soliton Fract. 126, 85–96 (2019)

    Article  ADS  Google Scholar 

  19. X.Y. Wang, G. Suo, Inf. Sci. 507, 16–36 (2020)

    Article  Google Scholar 

  20. Q. Lai, B. Norouzi, F. Liu, Chaos Soliton Fract. 114, 230–245 (2018)

    Article  ADS  Google Scholar 

  21. Q. Lai, Z.Q. Wan, P.D.K. Kuate et al., Commun. Nonlinear Sci. 89, 105341 (2020)

    Article  Google Scholar 

  22. F.H. Min, H.Y. Ma, Y.M. Lv, Eur. Phys. J-Spec. Top. 228, 1493–1514 (2019)

    Article  Google Scholar 

  23. M. Kountchou, P. Louodop, S. Bowong et al., Int. J. Bifurcat. Chaos. 26, 1–18 (2016)

    Article  Google Scholar 

  24. C.Q. Zhou, C.H. Yang, D.G. Xu et al., IEEE Access. 7, 52896–52902 (2019)

    Article  Google Scholar 

  25. C. Zhou, C.H. Wang, Y.C. Sun et al., Neurocomputing 403, 211–223 (2020)

    Article  Google Scholar 

  26. S. Khorashadizadeh, M.H. Majidi, Front. Inf. Tech. El. 19, 1180–1190 (2018)

    Article  Google Scholar 

  27. V. Resmi, G. Ambika, R.E. Amritkar, Phys. Rev. E 84, 046212 (2011)

    Article  ADS  Google Scholar 

  28. B. Zhen, Z.H. Li, Z.G. Song, Appl. Sci.-Basel 9, 2159 (2019)

    Article  Google Scholar 

  29. M. Iqbal, M. Rehan, K.S. Hong, Front. Neurorob. 12, 6 (2018)

    Article  Google Scholar 

  30. H.D. Li, X.L. Yang, Z.K. Sun, Nonlinear Dyn. 93, 1301–1314 (2018)

    Article  Google Scholar 

  31. C.G. Yang, S. Adhikari, H. Kim, Sci. China Inf. Sci. 61, 060427 (2018)

    Article  Google Scholar 

  32. S.K. Thottil, R.P. Ignatius, Nonlinear Dyn. 87, 1–21 (2016)

    Google Scholar 

  33. K. Usha, P.A. Subha, Chin. Phys. B 28, 020502 (2019)

    Article  ADS  Google Scholar 

  34. B.C. Bao, Q.F. Yang, D. Zhu et al., Nonlinear Dyn. 99, 2339–2354 (2020)

    Article  Google Scholar 

  35. H. Bao, Y.Z. Zhang, W.B. Liu et al., Nonlinear Dyn. 100, 937–950 (2020)

    Article  Google Scholar 

  36. S. Vaidyanathan, C.K. Volos et al., J. Eng. Technol. Rev. 8, 157–173 (2015)

    Article  Google Scholar 

  37. K. Murali, M. Lakshmanan, L.O. Chua, Int. J. Bifurcat. Chaos. 5, 563–71 (1995)

    Article  Google Scholar 

  38. G.Y. Peng, F.H. Min, Nonlinear Dyn. 90, 1607–1625 (2017)

    Article  Google Scholar 

  39. A.I. Ahamed, M. Lakshmanan, Int. J. Bifurcat. Chaos. 23, 1350098 (2013)

    Article  Google Scholar 

  40. B.C. Bao, L. Xu, N. Wang et al., AEÜ Int. J. Electron. Commun. 94, 26–35 (2018)

    Article  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Nature Science Foundation of China under Grant nos. 61971228 and 61871230, the Natural Science Foundations of Jiangsu Higher Education Institutions of China under Grant no. 19KJB520042, and the Postgraduate Research and Practice Innovation Program of Jiangsu of China under Grant No. KYCX20_1247.

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Authors and Affiliations

  1. School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing, 210023, China

    Yibo Wang, Fuhong Min, Yizi Cheng & Yiping Dou

Authors
  1. Yibo Wang
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  2. Fuhong Min
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  3. Yizi Cheng
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  4. Yiping Dou
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Contributions

YW and FM equally contributed to this work. YW carried out numerical simulations of synchronization and wrote the draft. FM developed theoretical approaches and revised the draft. YC and YD participated in discussing the contents.

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Correspondence to Fuhong Min.

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Wang, Y., Min, F., Cheng, Y. et al. Dynamical analysis in dual-memristor-based FitzHugh–Nagumo circuit and its coupling finite-time synchronization. Eur. Phys. J. Spec. Top. 230, 1751–1762 (2021). https://doi.org/10.1140/epjs/s11734-021-00121-0

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