Dependence of the spiral rotation frequency on the surface curvature of reaction–diffusion systems

Abstract

The dynamic behaviour of spiral waves rotating on surfaces of curved reaction–diffusion systems depends strongly on the curvature of the surface. It was shown in an earlier experiment that a spiral in a Belousov–Zhabotinsky system on a paraboloid drifts to the point of highest Gaussian curvature, as predicted numerically and analytically. Beyond this, theoretical work predicts an increase of the rotation frequency of spiral waves with an increase in the curvature of the system surface (e.g., spirals on different spherical surfaces with decreasing radii). This behaviour leads to an additional term in the function for the rotation frequency proportional to the Gaussian curvature of the system. In this Letter we combine both effects to determine the curvature dependence of the spiral rotation frequency in curved reaction–diffusion systems. On a non-homogeneously curved surface, the spiral tip (the inner end of a spiral) drifts through regions with increasing surface curvature. Measurements of the rotation frequency performed during this propagation verify the predicted effect. The experimental data are confirmed by analytical results in the framework of the kinematic theory.