6533b870fe1ef96bd12d06b5
RESEARCH PRODUCT
ANALYTICAL DETERMINATION OF INITIAL CONDITIONS LEADING TO FIRING IN NERVE FIBERS
Stéphane BinczakJean-marie BilbaultSabir Jacquirsubject
StationarityBistability[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph][MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS][ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS][MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]01 natural sciencesStability (probability)010305 fluids & plasmasStanding waveOptics[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]0103 physical sciencesReaction–diffusion systemTraveling wave[MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph]0101 mathematicsEngineering (miscellaneous)PhysicsQuantitative Biology::Neurons and Cognitionbusiness.industry[SCCO.NEUR]Cognitive science/Neurosciencenerve fibersApplied Mathematics[SCCO.NEUR] Cognitive science/Neurosciencereaction-diffusion[ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph]Mechanics[PHYS.MPHY] Physics [physics]/Mathematical Physics [math-ph]010101 applied mathematicsModeling and Simulation[ SCCO.NEUR ] Cognitive science/Neuroscience[ PHYS.MPHY ] Physics [physics]/Mathematical Physics [math-ph]Action potential firingbusinessStationary solutionnerve fibers.description
International audience; An analytical solution characterizing initial conditions leading to action potential firing in smooth nerve fibers is determined, using the bistable equation. In the first place, we present a nontrivial stationary solution wave, then, using the perturbative method, we analyze the stability of this stationary wave. We show that it corresponds to a frontier between the initiation of the travelling waves and a decay to the resting state. Eventually, this analytical approach is extended to FitzHugh-Nagumo model.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2007-10-01 | International Journal of Bifurcation and Chaos |