Planar and screw-shaped solutions for a system of two reaction-diffusion equations on the circle
Matthias Büger · Discrete and Continuous Dynamical Systems · 2006
We describe the dynamics of a system of two reaction-diffusionequations on the circle. We show that the elements of the $\omega$-limitsets of every solution can be classified by the number of times whichthey wind around the circle line --- they look either flat or screw-shaped.We prove a Poincaré-Bendixson result. Furthermore, we give a criterionunder which screw-shaped stationary or periodic solutions areunstable.