Author

Shawna Nelson

Abstract

We investigate a delay differential equation system version of a model designed to describe finite time population collapse.

The most commonly utilized population models are presented, including their strengths, weaknesses and limitations.

We introduce the Basener-Ross model, and implement the Hopf bifurcation test to identify whether there is a Hopf bifurcation in this system.

We attempt to improve upon the Basener-Ross model (which uses ordinary differential equations) by introducing delay differential equations to account for the gestational period of humans.

We utilize the singularity-removing transformation of the original Basener-Ross system for the delay differential equation system as well. The new system is shown to have a Hopf bifurcation. We also investigate how the bifurcation diagram of the original ODE model changes with the introduction of delays.

Publication Date

7-2013

Document Type

Thesis

Student Type

Graduate

Degree Name

Applied and Computational Mathematics (MS)

Department, Program, or Center

School of Mathematical Sciences (COS)

Advisor

Tamas Wiandt

Advisor/Committee Member

David Ross

Advisor/Committee Member

Ephraim Agyingi

Campus

RIT – Main Campus

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