Universal limit of spiral wave propagation in excitable media

We demonstrate that for a large class of excitable media the minimum excitability required for spiral wave propagation follows the universal scaling law ${\mathrm{\Delta }}_{\min }$=const×${\mathrm{\varepsilon }}^{1/3}$, where ɛ is the usual small parameter associated with the abruptness of excitation. The prefactor of the scaling law is obtained by solving the free-boundary problem of wave propagation. The quantitative validity of the free-boundary formulation is tested for the first time by direct comparison with the results of numerical simulation of a specific two-variable model of excitable kinetics.