Stable three-dimensional action potential circulation in the FitzHugh-Nagumo model

Abstract Excitable media generally support vortex rings of self-excitation. Depending on the exact nature of the medium, such a ring may expand or contract, possibly to a stable radius. We describe one such case encountered during numerical experiments on a simple model of electrophysiological excitability in nerve and cardiac muscle membrane. The ring's rate of shrinkage depends parabolically on curvature and on proximity to other rings. The vortex period also depends on curvature, so rings of different sizes compete for territory. We associate the stability of the ring with repulsive forces which we show are present between two-dimensional rotors. The observed minimal distance for repulsion agrees with the stable radius of the vortex ring.

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