Qualitative analysis of a model generating long potential waves in Ba-treated nerve cells. II. Complete system
✍ Scribed by José Argémi; Maurice Gola; Hélène Chagneux
- Publisher
- Springer
- Year
- 1980
- Tongue
- English
- Weight
- 768 KB
- Volume
- 42
- Category
- Article
- ISSN
- 1522-9602
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✦ Synopsis
This paper deals with a model describing the behavior of barium-treated Apalysia neurons. The model is represented by a dynamical system, so-called "complete system", defined in R 4 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 R 3, associgted 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.