Instabilities of a propagating pulse in a ring of excitable media

Abstract

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.