Reaction-diffusion equations on a sphere: Meandering of spiral waves

Abstract

Numerical integration of an excitable reaction-diffusion (RD) system on a sphere is presented. The evolution of counterrotating double spiral waves on this manifold is studied and it is shown that tips of the spiral can either perform a meandering motion or rigidly rotate around a fixed center, depending on the system control parameter. This transition in dynamics is also illustrated by considering the phase plane of the solutions of the RD system.