Mathematical Sciences: Wave Propagation in Excitable Media

研究者研究了心脏传导系统的两种模型。结合这些模型，他研究了行波解的存在性，并研究了行波的稳定性和分岔性。他寻求一种简化版的Beeler-Reuter哺乳动物心室纤维模型，该模型既保留了定性意义，又激发了分析性的见解，并计划将完整模型和简化模型进行比较。分析和计算工具都将在项目中使用。诸如此类的数学模型在研究心脏的行为方面非常有用。该项目的研究将有助于更好地理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.