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.
Library of Congress Subject Headings
Delay differential equations; Population--Mathematical models
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
Recommended Citation
Nelson, Shawna, "Population Modeling with Delay Differential Equations" (2013). Thesis. Rochester Institute of Technology. Accessed from
https://repository.rit.edu/theses/9078
Campus
RIT – Main Campus
Plan Codes
ACMTH-MS
