Bifurcation of Rotating Wave Solutions in Reaction-Diffusion Systems on a Circle

Abstract The existence of rotating wave solutions of a general reaction-diffusion system with nonlocal interaction on a circle are proved using a new bifurcation approach with two parameters, and a normal form for the rotating wave bifurcations is also developed to compute the direction of the bifurcation diagram. Theoretical results are applied to two model systems for the existence of rotating waves which are further verified by numerical simulations.