Diffusive Effects on Dispersion in Excitable Media

Abstract

Perturbation and numerical methods are used to study traveling and standing wave solutions for a system of reaction-diffusion equations modeled after excitable media and the effect of variation of the diffusion coefficients. It is shown that traveling waves and standing waves can coexist and that as a certain diffusion coefficient is varied a branch of traveling waves can bifurcate from a branch of standing waves, providing a transition between only traveling solutions in one limit and only standing waves in the other limit. Key words. traveling waves, standing waves, bifurcation, dispersion reaction-diffusion equations, singular perturbation