Mathematical Sciences: Mathematical Studies of Wave Propagation in Excitable Media

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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.