Spiral waves in the Belousov-Zhabotinskii reaction
The beautiful spiral waves of oxidation in the Belousov-Zhabotinskii reaction are the source of many interesting and important questions about periodic structures in excitable media. It has long been known that these spirals are similar to involutes of circles, at least some distance from the center, but until now, no way has been known to determine the correct wavelength and frequency. In this paper, we show that the parameters of a spiral wave can be viewed as eigenvalues of a problem with unique solution. The critical ingredients of the theory are the effects of curvature on the propagation of wave-fronts in two-dimensional media, and the dispersion of plane waves. Our analytical results are shown to be in good agreement with experimental data for the Belousov-Zhabotinskii reaction.
scientific article; zbMATH DE number 3987814