Canard Traveling Waves in a Reaction–Diffusion Model

The paper deals with the canard traveling waves in a reaction-diffusion model. The use of the geometric theory of invariant manifolds allows us to simplify the traveling wave problem of the original PDE system. We are focused on point-to-periodic traveling waves. It is shown that the profile of such waves is a canard. Canard traveling waves are critical waves since they separate waves with qualitatively different behaviors.