WAVE FRONT PROPAGATION AND ITS FAILURE IN COUPLED SYSTEMS OF DISCRETE BISTABLE CELLS MODELLED BY FITZHUGH-NAGUMO DYNAMICS

We discuss wave front propagation and its failure for the discrete FitzHugh-Nagumo system. We show, using a new comparison theorem, that wave front propagation is blocked for d, the coupling coefficient, sufficiently small and propagation must occur for d sufficiently large. Our numerical simulations confirm the analytical findings. We also give a numerical estimate for the speed of propagating waves as a function of d.