Date of Award

12-2015

Degree Type

Thesis

Degree Name

Master of Science

Major

Mathematics

Major Professor

Xiaopeng Zhao

Committee Members

Suzanne Lenhart, Charles Collins

Abstract

In this thesis, we study the nonlinear dynamics of calcium cycling within a cardiac cell. We develop piecewise smooth mapping models to describe intracellular calcium cycling in cardiac myocyte. Then, border-collision bifurcations that arise in these piecewise maps are investigated. These studies are carried out using both one-dimensional and two-dimensional models. Studies in this work lead to interesting insights on the stability of cardiac dynamics, suggesting possible mechanisms for cardiac alternans. Alternans is the precursor of sudden cardiac arrests, a leading cause of death in the United States.

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