Some Geometry of Cardiac Arrhythmias
May 22, 1997
Bailey Hall 102
Refreshments in the common room at 1:15
A hybrid of two familiar one-dimensional dynamical systems, pieced together with a discontinuity, exhibits two families of periodic windows, each with subfamilies organized by a Farey tree. We show the hybrid has asymptotic dynamics equivalent to those of a circle map that is not onto, and that the combinatorics of these windows are determined by those of inverse orbits exiting the image of the circle map. As a consequence, we derive simple rules for the symbolic dynamics of the window openings and closings. These lead to interative schemes for computing the window sizes, and several scalings are exhibited. Finally, we show this map is equivalent to a cardiac arrhythmia model proposed by Leon Glass and we illustrate the robustness of the phase-locking regimes determined by the windows.
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