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Instabilities in the circulation of a pulse in a ring of excitable cardiac tissue are analyzed using two different formulations: (1) a reaction-diffusion partial differential equation (PDE) model for cardiac electrical activity using the Beeler-Reuter equations to represent ionic currents in the cardiac cells; (2) a neutral delay-differential equation that we propose as a model for the PDE. Stability analysis and numerical simulation of the delay equation agree with results from simulations of the PDE model.
Courtemanche et al. (Mon,) studied this question.