Spiral waves on circular and spherical domains of excitable medium

Abstract The evolution of spiral waves on a circular domain and on a spherical surface is studied by numerical integration of a reaction-diffusion system. Two different asymptotic regimes are observed for both domains. The first regime is a rigid rotation of an excitation wave around the symmetry axis of the domain. The second one is a compound rotation including a drift of the rotation center of the spiral wave either along the boundary of the disk or along the equator of the sphere. In this case the shape of the wave and its rotation velocity are periodically changing in time. Simplified analytical estimates are presented to describe the rigid rotation. The computational results are complemented by experimental observation of spiral wave evolution in a small circular domain of a thin layer of Belousov-Zhabotinsky reagent.

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