Abstract
We explain the phenomenon of hypermeander of spiral waves, observed in numerical with various models of excitable media, as a chaotic attractor in the quotient system with respect to the Euclidean group. Such an attractor should lead to a motion of the spiral wave tip analogous to that of a Brownian particle, with mean square of displacement of the tip growing linearly at large times. This prediction is confirmed by numerical experiments with hypermeandering spiral waves.
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