Mathematical Sciences: Wave Propagation in Excitable Media

研究人员研究了心脏传导系统的两个模型。结合这些模型，他研究了行波解的存在性，并研究了行波解的稳定性和分叉。他为哺乳动物的心室纤维寻找简化版本的Beeler-Reuters模型，该模型保留了定性意义，同时激发了分析洞察力，并计划在完整模型和简化模型之间进行比较。该项目将同时使用分析和计算工具。像这样的数学模型在研究心脏的行为方面很有用。该项目的研究有助于更好地了解心脏电动力学和心跳异常。

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.