Year of Publication


Season of Publication


Paper Type

Master's Thesis


College of Arts and Sciences

Degree Name

Master of Science in Mathematical Sciences (MS)


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


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.