Title

A Qualitative Analysis of Differential Equations of Population Dynamics

Document Type

Thesis

Publication Date

1994

Advisor

Gary Brown

Abstract

An exploration of systems of equations modeling closed hypothetical ecosystems. Models are formed from biological assumptions about population. Models are constructed by combining or modifying simpler systems. The simple models used in constructing systems are the logistic, competition, and Lotka-Volterra models. Eigenvalues and eigenvectors are used to prove some results about the equilibria of the systems. Geometric perspectives of the systems are used to develop the intuitive approach of the work. Examples of graphed systems are included. Partial results are proven. Conjectures are formed. Difficulties in the work are described and suggestions for further work are given.

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