THEORY OF THE SPIRAL CORE IN EXCITABLE MEDIA

A rigorous asymptotic spiral solution to an excitable reaction diffusion system is found by separating space into two scaling regions: an ''outer region'', having the same spatial scaling as the overall spiral structure, which exhibits a singularity at the spiral tip; and a ''core'' region around the spiral tip, where space is scaled so as to resolve the tip singularity. The stability of the spiral structure is investigated for both the outer region, which is found to possess no intrinsic instability, and the core region which is found to be unstable. Both the zero and small diffusion systems are found to exhibit qualitatively similar behaviour. The implication of these results for both experiment and simulation, in particular within the context of the observed ''meandering'' instability, are addressed.