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.
Applied and Computational Mathematics (MS)
Department, Program, or Center
School of Mathematical Sciences (COS)
Nelson, Shawna, "Population Modeling with Delay Differential Equations" (2013). Thesis. Rochester Institute of Technology. Accessed from
RIT – Main Campus