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.

• Received 17 September 2002

DOI:https://doi.org/10.1103/PhysRevE.67.036105