Velocity Selection in Two-Dimensional Excitable Media: From Spiral Waves to Retracting Fingers

Abstract

Spiral waves in excitable media are typically observed to rotate at a unique angular frequency ω around an effective hole region of radius ro. We investigate the selection problem for ro and ω in the large ro limit of the free-boundary problem of wave propagation in excitable media for the case where the recovery variable is non-diffusive. Analytical forms are derived for the dependence of ro and ω on the usual small parameter e (which measures the abruptness of excitation) and a parameter A which measures the excitability of the medium. Where spiral wave solutions cease to exist we find a new class of solutions to the free-boundary problem analogous in shape to the Saffman-Taylor fingers of viscous hydrodynamics. These solutions correspond physically to wave fronts with a retracting tip structure.