Spirals in excitable media. II: Meandering transition in the diffusive free-boundary limit

In this paper we present a numerical stability calculation for steadily rotating spirals in an excitable medium. While experiments, as well as numerical simulations of two-field reaction-diffusion models have shown the existence of a Hopf bifurcation from steady rotations to a meandering state, all the analytical approaches so far have failed to predict this transition. This mismatch between analysis and simulations raises the question whether meandering critically depends on the finite diffusivity of the interface separating between the excited and the refractory phases. Our calculations show that this is not the case. The meandering transition takes place even in the limit of an infinitely sharp interface. The boundaries of the meandering transition as function of the model parameters are traced. We discuss possible explanations for the failure of previous analytical approaches.