6533b852fe1ef96bd12aa356

RESEARCH PRODUCT

EMERGENCE OF TRAVELLING WAVES IN SMOOTH NERVE FIBRES

Jean-marie BilbaultJean-paul GauthierSabir JacquirStéphane Binczak

subject

StationarityBistability[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS][ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS][ NLIN.NLIN-CD ] Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD][MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]01 natural sciencesNerve fibresStanding waveOptics[ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP]0103 physical sciencesTraveling wave[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]Discrete Mathematics and Combinatorics[MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]0101 mathematics010306 general physicsProjected dynamicsPhysicsSeparatrixbusiness.industry[SCCO.NEUR]Cognitive science/NeuroscienceApplied Mathematics[SCCO.NEUR] Cognitive science/NeuroscienceDiagramDynamics (mechanics)Mechanics010101 applied mathematics[NLIN.NLIN-CD] Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD]Amplitude[NLIN.NLIN-CD]Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD][ SCCO.NEUR ] Cognitive science/NeuroscienceAction potential firingbusinessAnalysis

description

International audience; 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.

yearjournalcountryeditionlanguage
2008-06-01
https://hal-univ-bourgogne.archives-ouvertes.fr/hal-00583779/file/DCDS_2008.pdf