ANALYTICAL DETERMINATION OF INITIAL CONDITIONS LEADING TO FIRING IN NERVE FIBERS

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

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

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.

Mots clés: nerve fibers; Stationarity; reaction-diffusion; nerve fibers.

Domaines: Sciences cognitives; Neurosciences; Physique [physics]; Physique mathématique [math-ph]; Mathématiques [math]; Physique mathématique [math-ph]; Mathématiques [math]; Systèmes dynamiques [math.DS]

Sabir Jacquir, Stéphane Binczak, Jean-Marie Bilbault. ANALYTICAL DETERMINATION OF INITIAL CONDITIONS LEADING TO FIRING IN NERVE FIBERS. International journal of bifurcation and chaos in applied sciences and engineering , 2007, 17 (10), pp.3697-3701. ⟨hal-00584230⟩