Date of Award

2008

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Bioinformatics & Computational Biology

First Advisor

Eric R. Kaufmann

Abstract

In this work, the theory of time scales calculus that we will employ is developed, as derivatives, integrals, and fundamental results are introduced. When necessary for subsequent discussion, other results are presented. The Hilger Complex Plane, the time scale exponential function, and its properties are given, as is a generalization of the variation of constants formula. The discrete and continuous Malthus population model, and the discrete and continuous Verhulst population models are investigated and analyzed. A unified and extended version of both models is developed and criteria for stability of critical solutions is presented. We investigate the relationship between both models through their generalized counterparts via different time scales. These include, but are not limited to the integers, [special characters omitted], and the reals, [special characters omitted]. Discrepancies and similarities between the original models and the generalized models are studied by applying both to classic examples of population data. We then use these results to consider the dynamics of emigration and harvesting. Finally, we consider a solution matching technique for finding solutions to a system of three population models on a time scale.

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