Skip to main content
SpringerLink
Log in

Bifurcations of oscillations of the membrane potential and the use of mappings for modeling electrically coupled neurons

  • Published:
Radiophysics and Quantum Electronics Aims and scope

Abstract

In this paper, we present the results of a qualitative analysis of a generalized system of three differential equations that represent the neuron model. The main nontrivial bifurcation sets leading to the appearance of complex motions, i.e., bursts, are given. A two-dimensional mapping that models the flows generated by this system, which is considered to be the simplest model of a neuron, is proposed. The chaotic dynamics of diffusely coupled neurons is studied using the coupled mappings.

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. L. Hodgkin and A. F. Huxley,J. Physiol.,117, 500 (1952).

    Google Scholar 

  2. J. L. Hindmarsh and R. M. Rose,Proc. Roy. Soc. London Ser. B,221, 87 (1984).

    ADS  Google Scholar 

  3. T. R. Chay,Physica D,16 233 (1985).

    Article  MATH  ADS  Google Scholar 

  4. V. Belykh, I. Belykh, M. Colding-Joergensen, and E. Mosekilde, “Homoclinic bifurcations of cell models with bursting oscillations,”Physica D, 1997 (in press).

  5. Y. S. Fan and T. R. Chay,Biol. Cyber.,71, 417 (1994).

    MATH  Google Scholar 

  6. V. N. Belykh and Yu. S. Chertkov,Boundary-Value Problems [in Russian] (1980).

  7. G. D. Abarbanel, M. I. Rabinovich, A.I. Sel’verston, M. V. Bazhenov, R. Khuerta, M. M. Sushchik, and L. L. Rubchinskii,Usp. Fiz. Nauk,166, 3 (1996).

    Article  Google Scholar 

  8. Ya. I. Mol’kov, M. I. Rabinovich, and M. M. Sushchik,Vestn. Nizh. Nov. Gos. Univ.,1, 15 (1996).

    Google Scholar 

  9. V. I. Arnold, V. S. Afraymovich, Yu. S. Il’yashenko, and L. P. Shil’nikov,Sovr. Prob. Mat., Fund. Napr., VINITI,5, 284 (1986).

    Google Scholar 

  10. K. Kaneko,Physica D,55, 368 (1992).

    Article  ADS  MATH  Google Scholar 

Download references

Authors
  1. I. V. Belykh
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Lobachevsky State Univesity of Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 12, pp. 1572–1580, December, 1998.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Belykh, I.V. Bifurcations of oscillations of the membrane potential and the use of mappings for modeling electrically coupled neurons. Radiophys Quantum Electron 41, 1066–1071 (1998). https://doi.org/10.1007/BF02676504

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02676504

Keywords

Search

Navigation