Abstract
We use our recent exactly solvable model of excitable media with nondiffusive control kinetics to study periodic wave trains in an excitable medium. We explicitly find restitution and dispersion curves for such a medium that are protocol independent. We also introduce an approximate stability criterion for periodic waves, which is based on the solitary pulse stability. Using our analytical periodic solutions as the initial conditions in our numerical experiments we demonstrate that this criterion indeed determines the minimal wavelength and propagation velocity below which both a solitary pulse and a periodic wave train quickly die.
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