Entrainment and termination of reentrant wave propagation in a periodically stimulated ring of excitable media

Excitable media, such as nerve, heart, and the Belousov-Zhabotinsky reaction, exhibit a large excursion from equilibrium in response to a small but finite perturbation. Assuming a one-dimensional ring geometry of sufficient length, excitable media support a periodic wave of circulation. In analogy with earlier results found from the periodic stimulation of oscillations in ordinary differential equations, the effects of periodic stimulation of the periodically circulating wave can be described by a one-dimensional map called the Poincar\'e map. Depending on the period and intensity of the stimulation as well as its initial phase, either entrainment or termination of the original circulating wave is observed. These phenomena are directly related to clinical observations concerning periodic stimulation of a class of cardiac arrhythmias caused by reentrant wave propagation in the human heart. {} 1996 The American Physical Society.