STATIONARY WAVE SOLUTIONS OF A SYSTEM OF REACTION-DIFFUSION EQUATIONS DERIVED FROM THE FITZHUGH-NAGUMO EQUATIONS

The authors consider an extension of the FitzHugh-Nagumo model, namely the system u//t equals D//1u//x//x plus f(u) minus w, w//t equals D//2w//x//x plus epsilon (u minus gamma w), where epsilon greater than O, gamma greater than O,D//1 greater than O, D//2 greater than O and f(u) is cubic. We allow gamma to be large which implies that there are three constant solutions. They show that over an appropriate range of parameters the system has time independent pulse solutions and an infinite number of periodic solutions. Depending on the particular choice of parameters, it is shown that the pulse solution leads to either the first constant solution or the third constant solution.