Meandering instability of a spiral interface in the free boundary limit.

Abstract

The two-component reaction-diffusion excitable medium is treated numerically in the free boundary limit for the fast field. We find that the spiral interface is stable for a sufficiently high diffusion constant of the slow field. The spiral wave (interface) undergoes a core-meander instability via a forward Hopf bifurcation as the diffusion constant decreases. A further decrease of the diffusion constant is found to result in the onset of hypermeandering and spiral breakup. We demonstrate quantitative convergence of the dynamics of reaction-diffusion system to its free boundary limit.