McKean caricature of the FitzHugh-Nagumo model: Traveling pulses in a discrete diffusive medium

Arnaud Tonnelier (1)

1 LCN - EPFL - Laboratory of Computational Neuroscience

This paper investigates traveling wave solutions of the spatially discrete reaction-diffusion systems whose kinetics are modeled by the McKean caricature of the FitzHugh-Nagumo model. In the limit of a weak coupling strength, we construct the traveling wave solutions and obtain the critical coupling constant below which propagation failure occurs. We report the existence of two different pulse traveling waves with different propagation speeds. Analytical results on the wave speed are obtained. Earlier results on propagation in the bistable medium are found as a limiting regime of our analysis.

Mots clés: Discrete diffusive coupling; Pulse propagation; McKean model

Domaines: Systèmes dynamiques [math.DS]

Arnaud Tonnelier. McKean caricature of the FitzHugh-Nagumo model: Traveling pulses in a discrete diffusive medium. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2003, pp.036105. ⟨hal-00393692⟩