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Date of Award

4-1997

Degree Type

Thesis

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

Supervisor

G.S.K. Wolkowicz

Abstract

We consider a model of the chemostat that involves a three species food chain with no imposed periodicities. The bottom trophic level species depends on a single, essential, growth-limiting nutrient. For a particular choice of prototype response functions, numerical simulations exhibit complicated dynamical behavior for reasonable parameter values. Using bifurcation theory methods we show the possibility of chaotic dynamics in a neighborhood of a particular equilibrium point. Moreover, we examine the role of each of the response functions with respect to the dynamics (i.e. chaos) of the model by systematically changing one response function at a time from linear to a more biologically reasonable Michaelis-Menten response function.

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Mathematics Commons

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