Deterministic Brownian motion in the hypermeander of spiral waves

We explain the phenomenon of hypermeander of spiral waves, observed in numerical experiments 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. Copyright (C) 1998 Elsevier Science B.V.