Skip to main content
SpringerLink
Log in

Transient dynamics in a small ensemble of synaptically coupled Morris-Lecar neurons

  • Published:
Radiophysics and Quantum Electronics Aims and scope

We propose a new model of synaptic transmission on the basis of a FitzHugh–Nagumo system with nonlinear recovery. It is shown that the Morrice–Lecar neuron ensemble formed by such couplings shows various structurally stable regimes of transient dynamics in the form of sequential transitions between various metastable oscillatory states of the system.

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. O. Mazur and G. Laurent, Neuron, 48, No. 4, 661 (2005).

    Article  Google Scholar 

  2. M. Stopfer, V. Jayaraman, and G. Laurent, Neuron, 39, No. 6, 991 (2003).

    Article  Google Scholar 

  3. L. M. Jones, A. Fontanini, B. F. Sadacca, et al., Proc. Nat. Acad. Sci. USA, 104, No. 47, 18 (2007).

    Article  Google Scholar 

  4. M. Rabinovich, A.Volkovskii, P. Lecanda, et al., Phys. Rev. Lett., 87, 068 102 (2001).

    Article  Google Scholar 

  5. V. S. Afraimovich, V. P. Zhigulin, and M. I. Rabinovich, Chaos, 14, No. 4, 1123 (2001).

    Article  MathSciNet  ADS  Google Scholar 

  6. M. I.Rabinovich, R.Huerta, and V. S.Afraimovich, Phys. Rev. Lett., 97, 188 103 (2006).

    Article  Google Scholar 

  7. M. I. Rabinovich, R.Huerta, P.Varona, et al., Biological Cybernetics, 95, No. 95, 519 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  8. C.Morris and H. Lecar, Biophys. J., 35, 193 (1981).

    Article  ADS  Google Scholar 

  9. A. L. Hodgkin and A. F. Huxley, J. Physiol., 117, No. 4, 500 (1952).

    Google Scholar 

  10. X. Shi, Q. Lu, and G.Chen, Int. J. Bifurc. Chaos, 17, No. 12, 4355 (2007).

    Article  MATH  MathSciNet  Google Scholar 

  11. A.Borisyuk, A. Friedman, B. Ermentrout, and D.Terman, Tutorials in Mathematical Biosciences I, Springer, Berlin (2005).

    MATH  Google Scholar 

  12. M. I.Rabinovich, P.Varona, A. I. Selverston, and H. D. I. Abarbanel, Rev. Mod. Phys., 78, No. 4, 1213 (2006).

    Article  ADS  Google Scholar 

  13. V. I.Nekorkin, A. S.Dmitrichev, D. S. Shchapin, et al., Math. Model., 17, No. 6, 75 (2005).

    MATH  MathSciNet  Google Scholar 

  14. Yu. A. Mitropol’skii and O. B. Lykova, Integral Manifolds in Nonlinear Mechanics [in Russian], Nauka, Moscow (1973).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia

    V. I. Nekorkin, D. V. Kasatkin & A. S. Dmitrichev

Authors
  1. V. I. Nekorkin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. V. Kasatkin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. S. Dmitrichev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. I. Nekorkin.

Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 53, No. 1, pp. 51–59, January 2010.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nekorkin, V.I., Kasatkin, D.V. & Dmitrichev, A.S. Transient dynamics in a small ensemble of synaptically coupled Morris-Lecar neurons. Radiophys Quantum El 53, 45–52 (2010). https://doi.org/10.1007/s11141-010-9203-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11141-010-9203-2

Keywords

Search

Navigation