Emergence of travelling waves in smooth nerve fibres

S. Jacquir; S. Binczak; J. P. Gauthier; J. M. Bilbault

doi:10.3934/dcdss.2008.1.263

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2008, Volume 1, Issue 2: 263-272. Doi: 10.3934/dcdss.2008.1.263

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Emergence of travelling waves in smooth nerve fibres

1.
LE2I UMR CNRS 5158, Aile des Sciences de l’Ingénieur, Université de Bourgogne, BP 47870, 21078 Dijon Cedex

Received: September 30, 2006

Revised: April 30, 2007

Published: May 2008

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Abstract

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.

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Mathematics Subject Classification: Primary: 92C20, 35K57; Secondary: 58E30.

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