Mathematical Sciences: Wave Propagation in Excitable Media

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The investigator studies two models for the cardiac conduction system. In connection with these models he investigates the existence of travelling wave solutions and studies the stability and bifurcations of the waves. He seeks a simplified version of the Beeler-Reuter model for mammalian ventricular fibers that retains qualitative significance while provoking analytical insight, and plans comparisons between the full and the simplified model. Both analytical and computational tools will be employed in the project. Mathematical models such as these have been useful in studying the behavior of the heart. The research of this project may contribute to better understanding of heart electrodynamics and heartbeat abnormalities.