EMERGENCE OF TRAVELLING WAVES IN SMOOTH NERVE FIBRES

Sabir Jacquir (1) , Stéphane Binczak (1) , Jean-Paul Gauthier (1) , Jean-Marie Bilbault (1)

1 Le2i - Laboratoire Electronique, Informatique et Image [UMR6306]

An approximate analytical solution characterizing initial condi- tions leading to action potential ¯ring in smooth nerve ¯bres is determined, using the bistable equation. In the ¯rst place, we present a non-trivial sta- tionary 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.

Mots clés: Stationarity; Nerve fibres; Projected dynamics

Domaines: Systèmes dynamiques [math.DS]; Dynamique Chaotique [nlin.CD]; Equations aux dérivées partielles [math.AP]; Neurosciences

Sabir Jacquir, Stéphane Binczak, Jean-Paul Gauthier, Jean-Marie Bilbault. EMERGENCE OF TRAVELLING WAVES IN SMOOTH NERVE FIBRES. Discrete and Continuous Dynamical Systems - Series S, 2008, 1 (2), pp.263-272. ⟨hal-00583779⟩