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Qualitative analysis of a model generating long potential waves in Ba-treated nerve cells. II. Complete system

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Abstract

This paper deals with a model describing the behavior of barium-treatedApalysia neurons. The model is represented by a dynamical system, so-called “complete system”, defined in R4 and depending on a small parameter. The study of this system under zero membrane current conditions was performed with the use of the qualitative theory of singular perturbations. We show that this system has a stable periodic solution of the discontinuous type when the small parameter tends to 0+. A reduced system defined in R3, associated to the complete system was also studied: it corresponds to a constant activation of the inward current. We demonstrate that the corresponding hypothetical cell remains silent under zero current conditions.

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Authors and Affiliations

  1. C.N.R.S., Laboratoire de Mécanique et d'Acoustique, 31, chemin Joseph-Aiguier, 13274, Marseille Cédex 2, France

    José Argémi

  2. C.N.R.S., Institute de Neurophysiologie et de Psychophysiologie, 31, chemin Joseph-Aiguier, 13274, Marseille Cédex 2, France

    Maurice Gola & Hélène Chagneux

Authors
  1. José Argémi
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  2. Maurice Gola
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  3. Hélène Chagneux
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Argémi, J., Gola, M. & Chagneux, H. Qualitative analysis of a model generating long potential waves in Ba-treated nerve cells. II. Complete system. Bltn Mathcal Biology 42, 221–238 (1980). https://doi.org/10.1007/BF02464639

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  • DOI: https://doi.org/10.1007/BF02464639

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