Stable rotating waves in two-dimensional discrete active media

The existence and stability of stable rotating solutions (spiral waves) in a discrete system of coupled phase models is proven. Monotone methods are used to obtain existence and qualitative features of the solutions. An application of Fenichel's results for singular perturbation implies the existence for a one variable model for excitability. Numerical comparisons with the phase model and a realistic membrane model are made. A numerically computed Hopf bifurcation shows the existence of the `wobbling core' observed in spatially continuous models.