Mathematical Sciences: Mathematical Studies of Wave Propagation in Excitable Media

本项目是研究波在可激发介质中的传播，特别侧重于两个特定系统，即心脏传导系统和别洛乌索夫-扎博金斯基反应。在心脏传导方面的工作将包括对两种纤颤发作模型的研究，一种是基于心脏细胞的各向异性偶联，另一种是基于心脏细胞恢复的差异。研究还将探讨离散性对繁殖的影响，以及非均匀性对可兴奋细胞同步性的影响。对别洛乌索夫-扎博廷斯基反应的研究将集中在螺旋波和涡旋波的动力学上。最后，研究将包括可激介质中的其他现象，如驻波和呼吸波，以及它们与行波的关系。

This project is to study wave propagation in excitable media with special emphasis on two specific systems, namely, the cardiac conduction system, and the Belousov Zhabotinsky reaction. Work on the cardiac conduction will include an investigation of two models for the onset of fibrillation, one based on the anisotropic coupling of cardiac cells, and the other based on disparity of recovery of cardiac cells. The investigation will also explore the effect of discreteness on propagation, and the effect of inhomogeneity on the synchrony of excitable cells. The investigation of Belousov Zhabotinsky reaction will center on the dynamics of spiral and scroll waves. Finally, the investigation will include the study of other phenomena in excitable media such as standing waves and breathers, and their relationship with traveling waves.