Date Thesis Awarded

4-2014

Document Type

Honors Thesis

Degree Name

Bachelors of Science (BS)

Department

Mathematics

Advisor

Sarah Day

Committee Member

Lawrence Leemis

Committee Member

Mark Brush

Abstract

Modeling zooplankton dynamics accurately is increasingly important because zooplankton can have a critical impact on several environmental issues ranging from eutrophication to climate change. Because of the importance of zooplankton in marine ecosystems, there is a need to develop precise mathematical models. Most models, however, set zooplankton mortality as due to predation only. This approach is inaccurate as many zooplankton can die from non-predatory causes such as disease or starvation. Here we construct a model that includes both predatory and non-predatory zooplankton mortality rather than a linear differential equation model that relies on curve-fitting to data. Through MATLAB simulations, this theoretical nonlinear model was found to be a strongly contracting system even under certain amounts of stochastic influence. While a linear approach when modeling marine species is the natural first step, a nonlinear approach, which is based more on mathematical and ecological theories rather than curve-fitting, allows for more complicated and realistic dynamics in addition to more accurate predictions.

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