Existence of spiral waves in an oscillatory reaction-diffusion system

Rotating waves are proven to exist on the unit disk for an oscillatory reaction-diffusion equation with Neuman boundary conditions. The method of proof relies on a two-parameter shooting argument for the ensemble frequency and the radial derivative of the magnitude. Numerical solutions indicate that the waves are stable if the diffusion is sufficiently small. It is also shown that these solutions cease to exist for large diffusion. The origin of the rotating waves is discussed.