Spiral waves on static and moving spherical domains

Abstract

The FitzHugh–Nagumo-type model on static and periodically oscillating surface of the sphere is studied. The numerical investigation of the model is performed in both cases and detailed numerical results are presented for the two-arm spiral wave and its rotation on both manifolds. On the static surface, meandering waves are obtained and it is shown that these waves are stable. On the periodically oscillating surface, the initial excitation gives rise to an irregular (chaotic) meandering rotation, depending on the frequency and the amplitude of the oscillations.