Dynamics of scroll rings in a parameter gradient

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Abstract
Experimental observations of scroll rings in excitable media have shown that an externally applied parameter gradient can significantly alter the dynamics of the ring, leading to rotation of the plane of the ring, variations in its rate of collapse, and distortions in its shape. Here we propose a theory to account for these effects by extending the theory of local filament dynamics to include the influence of the parameter gradient. Numerical simulations using the FitzHugh-Nagumo equations show that the proposed theory works well when the differences in rotation periods at different parts of the filament are sufficiently small. When this condition does not hold, the theory must be modified to take into account nonlocal interactions.