Abstract: Identifying mechanisms for the onset of abnormal heart rhythms (arrhythmias) is an important component of ongoing research in electrophysiology.  Mathematically, arrhythmias such as ventricular tachycardia and fibrillation can be identified with spiral waves and spatiotemporal chaos, respectively.  Understanding the precursors of such arrhythmias is possible even if we restrict ourselves to an idealized one-dimensional fiber of cardiac cells. In this presentation, I will use asymptotic methods to reduce a standard Hodgkin-Huxley type PDE model of a cardiac fiber to a system of ODEs which is amenable to mathematical analysis.  My calculations exploit a particular feature of cardiac tissue known as electrical restitution:  the speed and duration of cardiac action potentials depends upon how [locally] well-rested the tissue is.  The kinematic model that I will introduce is far less computationally expensive than standard PDE models, making it feasible to run repeated numerical experiments.  I will discuss one such experiment:  the use of far-field pacing and feedback control to terminate chaos.