Structure of the Resonance Attractor for Spiral Waves in Excitable Media

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Abstract
Recent experiments in the light-sensitive Belousov-Zhabotinsky reaction have shown that a pulsatory modulation of excitability controlled by a feedback can force the spiral wave core to execute a circular trajectory around a fixed measuring point of the medium. A theory is developed to explain the existence and stability of this resonance attractor which is based on reducing the spiral wave dynamics to a low-dimensional map. The analysis of this map predicts the existence of a discrete set of stable circular trajectories in good quantitative agreement with numerical simulations of the two-component Oregonator model. Only a small part of this set has so far been observed experimentally.