An article by Kondo and Asai demonstrated that the pattern formation and change on the skin of tropical fishes can be predicted well by reaction-diffusion models of Turing type. As being observed, a common pattern structure is the rearrangement of stripe pattern, and defect like heteroclinic solution appeared between the patterns with different number of stripes. We consider FitzHugh-Nagumo type reaction-diffusion systems with anisotropic diffusion. Under a sufficient condition in diffusivity, we apply variational arguments to show the existence of standing waves joining with Turing patterns.
Communications in Partial Differential Equations, 36(6): 998-1015