Bulletin of Mathematical Biology

, Volume 42, Issue 2, pp 221–238 | Cite as

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

  • José Argémi
  • Maurice Gola
  • Hélène Chagneux


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.


Periodic Solution Singular Point Singular Perturbation Potential Wave Slow Manifold 
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Copyright information

© Society for Mathematical Biology 1980

Authors and Affiliations

  • José Argémi
    • 1
  • Maurice Gola
    • 2
  • Hélène Chagneux
    • 2
  1. 1.C.N.R.S.Laboratoire de Mécanique et d'AcoustiqueMarseille Cédex 2France
  2. 2.C.N.R.S.Institute de Neurophysiologie et de PsychophysiologieMarseille Cédex 2France

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