Mathematical Models in Population Dynamics

Date of Award

2011

Document Type

Thesis

Degree Name

Bachelors

Department

Natural Sciences

First Advisor

Yildirim, Necmettin

Keywords

Population Dynamics, Dynamical Systems, Mathematical Modeling, Population Ecology, Ecological Dynamics

Area of Concentration

Natural Sciences

Abstract

Population dynamics studies the changes in size and composition of populations through time, as well as the biotic and abiotic factors influencing those changes. For the past few centuries, ordinary differential equations (ODEs) have served well as models of both single-species and multispecies population dynamics. In this study, we provide a mathematical framework for ODE model analysis and an outline of the historical context surrounding mathematical population modeling. Upon this foundation, we pursue a piecemeal construction of ODE models beginning with the simplest one-dimensional models and working up in complexity into two-dimensional systems. Each modeling step is complimented with mathematical analysis, thereby elucidating the model�s behaviors, and allowing for biological interpretations to be established.

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