Second universal limit of wave segment propagation in excitable media

A free-boundary approach is applied to derive universal relationships between the excitability and the velocity and the shape of stabilized wave segments in a broad class of excitable media. In the earlier discovered low excitability limit wave segments approach critical fingers. We demonstrate the existence of a second universal limit (a motionless circular shaped spot) in highly excitable media. Analytically obtained asymptotic relationships and interpolation formula connecting both excitability limits are in good quantitative agreement with results from numerical simulations.