Year
2013
Season
Summer
Paper Type
Master's Thesis
College
College of Arts and Sciences
Degree Name
Master of Science in Mathematical Sciences (MS)
Department
Mathematics & Statistics
NACO controlled Corporate Body
University of North Florida. Department of Mathematics and Statistics
First Advisor
Dr. Mahbubur Rahman
Second Advisor
Dr. Adel Boules
Third Advisor
Dr. Ognjen Milatovic
Department Chair
Dr. Scott Hochwald
College Dean
Dr. Barbara A. Hetrick
Abstract
We first discuss some fundamental results such as equilibria, linearization, and stability of nonlinear dynamical systems arising in mathematical modeling. Next we study the dynamics in planar systems such as limit cycles, the Poincaré-Bendixson theorem, and some of its useful consequences. We then study the interaction between two and three different cell populations, and perform stability and bifurcation analysis on the systems. We also analyze the impact of immunotherapy on the tumor cell population numerically.
Suggested Citation
Ferrara, Joseph, "A Study of Nonlinear Dynamics in Mathematical Biology" (2013). UNF Graduate Theses and Dissertations. 448.
https://digitalcommons.unf.edu/etd/448