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Ordinary Differential Equations and Applied Dynamics Commons™
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Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
A Study Of Nonlinear Dynamics In Mathematical Biology, Joseph Ferrara
A Study Of Nonlinear Dynamics In Mathematical Biology, Joseph Ferrara
UNF Graduate Theses and Dissertations
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.