Graduation Semester and Year

2008

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Hristo Kojouharov

Abstract

Mathematical population models of nutrient recycling and allelopathy are presented. The chemostat limited-resource model forms the basis for each of the models, amended with the dynamics of nutrient recycling and allelopathy. Nutrient recycling considers the explicit mortality of the population as providing additional recycled nutrient available to the remaining organisms. Also considered is allelopathy in which one population produces a poison to increase the mortality of another population. In this study we explore allelopathy in which the poison producer increases toxicity as the nutrients are limited. In addition to the chemostat model, we also consider the associated gradostat, two chemostat devices in series. Local analysis and numerical simulations are presented for each of the models along with global results where available.

Disciplines

Mathematics | Physical Sciences and Mathematics

Comments

Degree granted by The University of Texas at Arlington

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Mathematics Commons

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