THE 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 meth od of proof relies on a two-parameter shooting argument for the ensemb le frequency and the radial derivative of the magnitude. Numerical sol utions indicate that the waves are stable if the diffusion is sufficie ntly small. It is also shown that these solutions cease to exist for l arge diffusion. The origin of the rotating waves is discussed.