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.
Bibliographical noteFunding Information:
Parts of this work were accomplished while R.K. was at Bell Laboratories. We thank H. Levine for many fruitful discussions. DAK thanks I. Aranson and I. Mitkov for discussions. We also thank the anonymous referee for his helpful comments. The work of DAK is supported in part by the Israel Science Foundation. RK is supported by the Applied Mathematical Sciences Subprogram of the Office of Energy Research, US Department of Energy, under Contract Number DE-AC03-76SF00098.