Nelson, Shawna. 2013 Population Modeling with Delay Differential Equations. Master of Science Thesis. Rochester Institute of Technology, Rechester NY USA.
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.
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