The European Physical Journal Special Topics

, Volume 228, Issue 10, pp 2053–2063 | Cite as

Memristor reduces conduction failure of action potentials along axon with Hopf bifurcation

  • Xinjing Zhang
  • Huaguang GuEmail author
  • Fuqiang Wu
Regular Article
Part of the following topical collections:
  1. Memristor-based Systems: Nonlinearity, Dynamics and Applications


Memristor has been identified to modulate electronic activities of the nervous system, and conduction failure of action potentials along axon has been identified to play important roles in information transition related to pathological pain. In the present paper, the influences of the memristor on the conduction failure induced by the external stimulation with high frequency are investigated. After introducing electromagnetic induction mediated by memristor into Hodgkin-Hexley (HH) model, the Hopf bifurcation advances with increasing depolarization current, and the membrane potential of the resting state near the bifurcation increases. Such two changes mainly lead to the decrease of conduction failure rate of action potentials along axon which is described with a network model composed of HH neurons. Moreover, the reduction of conduction failure rate induced by memristor is well interpreted with the nonlinear dynamics near the bifurcation point, for example, the dynamics of the current threshold to evoke the second action potential from the after-potential following the first one. The results present that memristor can promote the conduction ability of action potentials along axon, which presents a novel function of memristor and contributes to the information transmission related to pathological pain in the nervous system.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    L.O. Chua, IEEE Trans. Circ. Theor. 18, 507 (1971)CrossRefGoogle Scholar
  2. 2.
    Y. Babacan, F. Kacar, K. Gürkan, Neurocomputing 203, 86 (2016)CrossRefGoogle Scholar
  3. 3.
    A.L. Wu, Z.G. Zeng, X.S. Zhu, J.N. Zhang, Neurocomputing 74, 3043 (2011)CrossRefGoogle Scholar
  4. 4.
    J. Kengne, A.N. Negou, D. Tchiotsop, Nonlinear Dyn. 88, 2589 (2017)CrossRefGoogle Scholar
  5. 5.
    R. Rakkiyappan, G. Velmurugan, X.D. Li, D. O’Regan, Neural Comput. Appl. 27, 629 (2016)CrossRefGoogle Scholar
  6. 6.
    V.T. Pham, C. Volos, L.V. Gambuzza, Sci. World J. 2014, 368986 (2014)CrossRefGoogle Scholar
  7. 7.
    D.B. Strukov, G.S. Snider, D.R. Stewart, R.S. Williams, Nature 453, 80 (2008)ADSCrossRefGoogle Scholar
  8. 8.
    S.H. Jo, T. Chang, I. Ebong, B.B. Bhadviya, P. Mazumder, L. Wei, Nano Lett. 10, 1297 (2010)ADSCrossRefGoogle Scholar
  9. 9.
    A. Thomas, J. Phys. D: Appl. Phys. 46, 093001 (2013)ADSCrossRefGoogle Scholar
  10. 10.
    J.F. Barry, M.J. Turner, J.M. Schloss, D.R. Glenn, Y. Song, M.D. Lukin, H. Park, R.L. Walsworth, Proc. Natl. Acad. Sci. 49, 14133 (2016)ADSCrossRefGoogle Scholar
  11. 11.
    Z. Rostami, V.T. Pham, S. Jafari, F. Hadaeghi, J. Ma, Appl. Math. Comput. 338, 141 (2018)MathSciNetGoogle Scholar
  12. 12.
    M. Lv, C.N. Wang, G.D. Ren, J. Ma, X.L. Song, Nonlinear Dyn. 85, 1479 (2016)CrossRefGoogle Scholar
  13. 13.
    Y. Wang, J. Ma, Y. Xu, F.Q. Wu, P. Zhou, Int. J. Bifurc. Chaos 27, 1750030 (2017)CrossRefGoogle Scholar
  14. 14.
    F.Q. Wu, C.N. Wang, W.Y. Jin, J. Ma, Physica A 469, 81 (2017)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    G. Zhang, F.Q. Wu, T. Hayat, J. Ma, Commun. Nonlinear Sci. Numer. Simul. 65, 79 (2018)ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    L.L. Lu, J.B. Kirunda, Y. Xu, W.J. Kang, R. Ye, X. Zhan, Y. Jia, Eur. Phys. J. Special Topics 227, 767 (2018)ADSCrossRefGoogle Scholar
  17. 17.
    M.Y. Ge, Y. Xu, Z.K. Zhang, Y.X. Peng, W.J. Kang, L.J. Yang, Y. Jia, Eur. Phys. J. Special Topics 227, 799 (2018)ADSCrossRefGoogle Scholar
  18. 18.
    B.J. Roth, P.J. Basser, IEEE Trans. Biomed. Eng. 37, 588 (1990)CrossRefGoogle Scholar
  19. 19.
    S. Mostaghimi, F. Nazarimehr, S. Jafari, J. Ma, Appl. Math. Comput. 348, 42 (2019)MathSciNetGoogle Scholar
  20. 20.
    Z. Rostami, K. Rajagopal, A.J.M. Khalaf, S. Jafari, M. Perc, M. Slavinec, Physica. A 509, 1162 (2018)ADSCrossRefGoogle Scholar
  21. 21.
    F. Parastesh, H. Azarnoush, S. Jafari, B. Hatef, M. Perc, R. Repnik, Appl. Math. Comput. 350, 217 (2019)MathSciNetGoogle Scholar
  22. 22.
    B. Cao, L.N. Guan, H.G. Gu, Acta Phys. Sin. 67 240502 (2018) (in Chinese)Google Scholar
  23. 23.
    F. Nazarimehr, S.M.R.H. Golpayegani, B. Hatef, Eur. Phys. J. Special Topics 227, 697 (2018)ADSCrossRefGoogle Scholar
  24. 24.
    A.A. Faisal, S.B. Laughlin, PLoS Comput. Biol. 3, e79 (2007)ADSCrossRefGoogle Scholar
  25. 25.
    Y.G. Yao, J. Ma, Eur. Phys. J. Special Topics 227, 757 (2018)ADSCrossRefGoogle Scholar
  26. 26.
    A.L. Hodgkin, A.F. Huxley, J. Physiol. 117, 500 (1952)CrossRefGoogle Scholar
  27. 27.
    Z.R. Zhu, X.W. Tang, W.T. Wang, W. Ren, J.L. Xing, J.R. Zhang, J.H. Duan, Y.Y. Wang, X.Y. Jiao, S.J. Hu, Neurosignals 17, 181 (2009)CrossRefGoogle Scholar
  28. 28.
    W. Sun, B. Miao, X.C. Wang, J.H. Duan, W.T. Wang, F. Kuang, R.G. Xie, J.L. Xing, H. Xu, X.J. Song, C. Luo, S.J. Hu, Brain 135, 359 (2012)CrossRefGoogle Scholar
  29. 29.
    X.C. Wang, S. Wang, W.T. Wang, J.H. Duan, M. Zhang, X.H. Lv, C.X. Niu, C. Tan, Y.B. Wu, J. Yang, S.J. Hu, J.L. Xing, Pain 157, 2235 (2016)CrossRefGoogle Scholar
  30. 30.
    S.L. Guo, C.N. Wang, J. Ma, W.Y. Jin, Neurocomputing 216, 627 (2016)CrossRefGoogle Scholar
  31. 31.
    R. Follmann, E. Rosa, W. Stein, Phys. Rev. E 92, 032707 (2015)ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    S.Y. Zeng, Y. Tang, Phys. Rev. E 80, 021917 (2009)ADSCrossRefGoogle Scholar
  33. 33.
    A.L. Fitch, D. Yu, H.H.C. Iu, V. Sreeram, Int. J. Bifurc. Chaos 22, 8 (2012)CrossRefGoogle Scholar
  34. 34.
    B. Muthuswamy, Int. J. Bifurc. Chaos 20, 1335 (2010)CrossRefGoogle Scholar
  35. 35.
    Q.D. Li, H.Z. Zeng, J. Li, Nonlinear Dyn. 79, 2295 (2015)CrossRefGoogle Scholar
  36. 36.
    B. Ermentrout, Simulating, analyzing, and animating dynamical systems: A guide to XPPAUT for researchers and students (SIAM, Philadelphia, 2002)Google Scholar

Copyright information

© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Aerospace Engineering and Applied Mechanics, Tongji UniversityShanghai200092P.R. China

Personalised recommendations