American Institute of Mathematical Sciences

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June  2008, 1(2): 263-272. doi: 10.3934/dcdss.2008.1.263

Emergence of travelling waves in smooth nerve fibres

S. Jacquir 1, , S. Binczak 1, , J. P. Gauthier 1, and  J. M. Bilbault 1,

1. 

LE2I UMR CNRS 5158, Aile des Sciences de l’Ingénieur, Université de Bourgogne, BP 47870, 21078 Dijon Cedex, France, France, France, France

Received  October 2006 Revised  May 2007 Published  March 2008

An approximate analytical solution characterizing initial conditions leading to action potential firing in smooth nerve fibres is determined, using the bistable equation. In the first place, we present a non-trivial stationary solution wave. Then, we extract the main features of this solution to obtain a frontier condition between the initiation of the travelling waves and a decay to the resting state. This frontier corresponds to a separatrix in the projected dynamics diagram depending on the width and the amplitude of the stationary wave.
Keywords: nerve fibres, projected dynamics., stationarity.
Mathematics Subject Classification: Primary: 92C20, 35K57; Secondary: 58E3.
Citation: S. Jacquir, S. Binczak, J. P. Gauthier, J. M. Bilbault. Emergence of travelling waves in smooth nerve fibres. Discrete & Continuous Dynamical Systems - S, 2008, 1 (2) : 263-272. doi: 10.3934/dcdss.2008.1.263
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