PROPAGATING WAVES IN DISCRETE BISTABLE REACTION-DIFFUSION SYSTEMS

We consider a discrete bistable reaction-diffusion system modeled by N coupled Nagumo equations. We develop an asymptotic method to describe the phenomenon of propagation failure. The Nagumo model depends on tw o parameters: the coupling constant d and the bistability parameter a. We investigate the limit a --> 0 and d(a) --> 0 and construct traveli ng front solutions. We obtain the critical coupling constant d = d(a) above which propagation is possible and determine the propagation spe ed c = c(d) if d > d. We investigate two different cases for the init iation of a propagating front solution. Case 1 considers a uniform ste ady state distribution. A propagating front appears as the result of a fixed boundary condition. Case 2 also considers a uniform steady stat e distribution but a propagating front appears as the result of a loca lized perturbation.