The structure of the quiescent core in rigidly rotating spirals in a class of excitable systems

Abstract

We consider a class of excitable system whose dynamics is de- scribed by Fitzhugh-Nagumo (FN) equations. We provide a description for rigidly rotating spirals based on the fact that one of the unknowns develops abrupt jumps in some regions of the space. The core of the spiral is delim- ited by these regions. The description of the spiral is made using a mixture of asymptotic and rigorous arguments. Several open problems whose rigorous solution would provide insight in the problem are formulated.