The dispersion relation is the dependence of the velocity of periodic planar wave trains on their wavelength. We study the occurrence of a velocity gap in the dispersion relation in a bistable three component reaction-diffusion system modeling intracellular ${\mathrm{Ca}}^{2+}$ dynamics. In two spatial dimensions, localized pinned spirals are observed, if their wavelength falls into the dispersion gap. Destruction of free spirals occurs already for conditions where the asymptotic planar wave train exists and the dispersion gap is absent.

• Received 1 November 1999

DOI:https://doi.org/10.1103/PhysRevLett.84.4753