Bulletin of Mathematical Biology

, Volume 41, Issue 5, pp 665–686 | Cite as

Qualitative analysis of a model generating long potential waves in Ba-treated nerve cells—I. Reduced systems

  • José Argémi
  • Maurice Gola
  • Hélène Chagneux
Article

Abstract

This study is related to a model describing the behavior of barium-treatedAplysia neurons generating regular burst-plateau patterns. The model is represented by an autonomous dynamical system, defined inR 4 and depending on a small parameter. This paper is restricted to the qualitative study of three “reduced systems” deduced from the “complete system”. Part of the study is performed with the use of the qualitative theory of singular perturbations. The predicted behaviors are compared with experimental results.

Keywords

Periodic Solution Singular Point Outward Current Potential Wave Slow Manifold 

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Copyright information

© Society for Mathematical Biology 1979

Authors and Affiliations

  • José Argémi
    • 1
  • Maurice Gola
    • 2
  • Hélène Chagneux
    • 2
  1. 1.Laboratoire de Mécanique et d'AcoustiqueC.N.R.S.Marseille cédex 2France
  2. 2.Institut de Neurophysiologie et de PsychophysiologieC.N.R.S.Marseille cédex 2France

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