Skip to main content
SpringerLink
Log in

Effects of memristor-based coupling in the ensemble of FitzHugh–Nagumo elements

  • Regular Article
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

We consider a system of two identical FitzHugh–Nagumo elements with electrical and memristor-based couplings and study the effect of these couplings on the nature of neuron-like spiking regimes that were previously observed in such systems with only chemical excitatory couplings.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A.E. Pereda, Nat. Rev. Neurosci. 15, 250 (2014)

    Article  Google Scholar 

  2. V.S. Afraimovich, M.I. Rabinovich, P. Varona, Int. J. Bifurc. Chaos 14, 1195 (2004)

    Article  Google Scholar 

  3. T.A. Levanova, M.A. Komarov, G.V. Osipov, Eur. Phys. J. Special Topics 222, 2417 (2013)

    Article  ADS  Google Scholar 

  4. R. Reimbayev, I. Belykh, Int. J. Bifurc. Chaos 22, 1440013 (2014)

    Article  Google Scholar 

  5. B.K. Bera, D. Ghosh, M. Lakshmanan, Phys. Rev. E 93, 012205 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  6. A.R. Martin, P.A. Fuchs, D.A. Brown, M.E. Diamond, D.A. Weisblat, From neuron to brain, 5th edn. (Sinauer Associates, Sunderland, MA, 2011)

  7. B.W. Connors, M.A. Long, Annu. Rev. Neurosci. 27, 393 (2004)

    Article  Google Scholar 

  8. H.V. Wheal, A.M. Thomson, Neuroscience 13, 97 (1984)

    Article  Google Scholar 

  9. V. Zsiros, I. Aradi, G. Maccaferri, J. Physiol. 578, 527 (2007)

    Article  Google Scholar 

  10. D.G. Placantonakis, A.A. Bukovsky, S.A. Aicher, H.P. Kiem, J.P. Welsh, J. Neurosci. 26, 5008 (2006)

    Article  Google Scholar 

  11. C.E. Landisman, B.W. Connors, Science 310, 1809 (2005)

    Article  ADS  Google Scholar 

  12. J.S. Haas, B. Zavala, C.E. Landisman, Science 334, 389 (2011)

    Article  ADS  Google Scholar 

  13. J.S. Haas, C.M. Greenwald, A.E. Pereda, BMC Cell Biol. 17, 51 (2016)

    Article  Google Scholar 

  14. Z. Wang, R. Neely, C.E. Landisman, J. Neurosci. 35, 7616 (2015)

    Article  Google Scholar 

  15. J. O’Brien, Curr. Opin. Neurobiol. 29, 64 (2014)

    Article  Google Scholar 

  16. S.A. Bloomfield, B. Volgyi, Nat. Rev. Neurosci. 10, 495 (2009)

    Article  Google Scholar 

  17. B.W. Connors, Electrical signaling with neuronal gap junctions, in Connexins: A guide, edited by A. Harris, D. Locke (Humana Press/Springer, 2009), pp. 143–164

  18. A. Gelperin, J. Neurosci. 26, 1663 (2006)

    Article  Google Scholar 

  19. M.J. Kahana, J. Neurosci. 26, 1669 (2006)

    Article  Google Scholar 

  20. O. Paulsen, T.J. Sejnowski, J. Neurosci. 26, 1661 (2006)

    Article  Google Scholar 

  21. T.J. Sejnowski, O. Paulsen, J. Neurosci. 26, 1673 (2006)

    Article  Google Scholar 

  22. R. Reimbayev, K. Daley, I. Belykh, Phil. Trans. R. Soc. A 375, 20160282 (2017)

    Article  ADS  Google Scholar 

  23. N. Spruston, Neuron 31, 669 (2001)

    Article  Google Scholar 

  24. W. Singer, C.M. Gray, Annu. Rev. Neurosci. 18, 555 (1995)

    Article  Google Scholar 

  25. W. Singer, Neuron 24, 49 (1999)

    Article  Google Scholar 

  26. J. Ma, J. Tang, Nonlinear Dyn. 89, 1569 (2017)

    Article  Google Scholar 

  27. M. Lv, C.N. Wang, G.D. Ren, J. Ma, X.L. Song, Nonlinear Dyn. 85, 1479 (2016)

    Article  Google Scholar 

  28. M. Lv, J. Ma, Neurocomputing 205, 375 (2016)

    Article  Google Scholar 

  29. L.O. Chua, IEEE Trans. Circuit Theory 18, 507 (1971)

    Google Scholar 

  30. L.O. Chua, Nanotechnology 24, 1 (2013)

    Article  Google Scholar 

  31. S.H. Jo, T. Chang, I. Ebong, B.B. Bhadviya, P. Mazumder, W. Lu, Nano Lett. 10, 1297 (2010)

    Article  ADS  Google Scholar 

  32. M. Laiho, E. Lehtonen, in Proceedings IEEE of International Symposium on Circuits and Systems (ISCAS 2010) (2010), pp. 2051–2054

  33. B. Linares-Barranco, T. Serrano-Gotarredona, Nature Precedings 1 (2009)

  34. F. Wu, C. Wang, W. Jin, J. Ma, Physica A 469, 81 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  35. C.K. Volos, I.M. Kyprianidis, I.N. Stouboulos, E. Tlelo-Cuautle, S. Vaidyanathan, J. Eng. Sci. Technol. Rev. 8, 157 (2015)

    Article  Google Scholar 

  36. J. Ma, L. Mi, P. Zhou, Y. Xu, T. Hayat, Appl. Math. Comput. 307, 321 (2017)

    MathSciNet  Google Scholar 

  37. A.G. Korotkov, A.O. Kazakov, T.A. Levanova, G.V. Osipov, Commun. Nonlinear Sci. Numer. Simul. 71, 38 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  38. A. Destexhe, Z.F. Mainen, T.J. Sejnowski, Neural Comput. 6, 14 (1994)

    Article  Google Scholar 

  39. A.G. Korotkov, A.O. Kazakov, T.A. Levanova, G.V. Osipov, IFAC-PapersOnLine 51, 241 (2018)

    Article  Google Scholar 

  40. A. Riehle, S. Grun, M. Diesmann, Science 278, 1950 (1997)

    Article  ADS  Google Scholar 

  41. J. Fell, N. Axmacher, Nat. Rev. Neurosci. 12, 105 (2011)

    Article  Google Scholar 

  42. S.M. Montgomery, G. Buzsaki, Proc. Natl. Acad. Sci. 104, 14495 (2007)

    Article  ADS  Google Scholar 

  43. K. Lehnertz, S. Bialonski, M.T. Horstmann, D. Krug, A. Rothkegel, M. Staniek, T. Wagner, J. Neurosci. Methods 183, 42 (2009)

    Article  Google Scholar 

  44. I. Netoff, J. Schiff, J. Neurosci. 22, 7297 (2002)

    Article  Google Scholar 

  45. S. Majhi, M. Perc, D. Ghosh, Sci. Rep. 6, 39033 (2016)

    Article  ADS  Google Scholar 

  46. Q. Wang, M. Perc, Z. Duan, G. Chen, Phys. Rev. E 80, 026206 (2009)

    Article  ADS  Google Scholar 

  47. Q.Y. Wang, M. Aleksandra, M. Perc, Chin. Phys. B 20, 040504 (2011)

    Article  ADS  Google Scholar 

  48. X.-J. Wang, J. Rinzel, Neural Comput. 4, 84 (1992)

    Article  Google Scholar 

  49. M.J. Sharifi, Y.M. Banadaki, J. Circuits Syst. Comput. 19, 407 (2010)

    Article  Google Scholar 

  50. H.P. Schwan, Biological engineering (McGraw-Hill Companies, New York, 1969)

  51. M. Krupa, P. Szmolyan, J. Differ. Equ. 174, 312 (2001)

    Article  ADS  Google Scholar 

  52. T.A. Levanova, A.O. Kazakov, A.K. Korotkov, G.V. Osipov, Izvestiya Vysshikh Uchebnykh Zavedeniy Prikladnaya Nelineynaya Dinamika 26, 101 (2018)

    Google Scholar 

  53. L.P. Shilnikov, Sov. Mat. Dok. 6, 163 (1965)

    Google Scholar 

  54. L.P. Shilnikov, Mat. Sb. 81, 92 (1970)

    MathSciNet  Google Scholar 

  55. A. Mishra, S. Saha, M. Vigneshwaran, P. Pal, T. Kapitaniak, S.K. Dana, Phys. Rev. E 97, 062311 (2018)

    Article  ADS  Google Scholar 

  56. P. Gaspard, S. Gonchenko, Nonlinearity 10, 409 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  57. D.S. Reich, F. Mechler, K.P. Purpura, J.D. Victor, J. Neurosci. 20, 1964 (2000)

    Article  Google Scholar 

  58. Y.V. Bakhanova, A.O. Kazakov, A.G. Korotkov, T.A. Levanova, Eur. Phys. J. Special Topics 227, 959 (2018)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lobachevsky State University of Nizhny Novgorod, 23 Prospekt Gagarina, Nizhny Novgorod, 603950, Russia

    Alexander G. Korotkov & Tatiana A. Levanova

  2. National Research University Higher School of Economics, 25/12 Bolshaya Pecherskaya Ulitsa, 603155, Nizhny Novgorod, Russia

    Alexey O. Kazakov

Authors
  1. Alexander G. Korotkov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alexey O. Kazakov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tatiana A. Levanova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tatiana A. Levanova.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Korotkov, A.G., Kazakov, A.O. & Levanova, T.A. Effects of memristor-based coupling in the ensemble of FitzHugh–Nagumo elements. Eur. Phys. J. Spec. Top. 228, 2325–2337 (2019). https://doi.org/10.1140/epjst/e2019-900053-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2019-900053-9

Search

Navigation