Rich dynamics have been demonstrated when a discrete time delay is introduced in a simple
predator-prey system. For example, Hopf bifurcations and a sequence of period doubling bifurcations that appear
to lead to chaotic dynamics have been observed. In this thesis we consider two different
predator-prey models: the classical Gause-type predator-prey model and the chemostat predator-prey model.
In both cases, we explore how different ways of modeling the time between the first contact of the predator
with the prey and its eventual conversion to predator biomass affects the possible range of dynamics
predicted by the models. The models we explore are systems of integro-differential equations with
delay kernels from various distributions including the gamma distribution of different orders, the uniform
distribution, and the Dirac delta distribution. We study the models using bifurcation theory
taking the mean delay as the main bifurcation parameter. We use both an analytical approach and a
computational approach using the numerical continuation software XPPAUT and DDE-BIFTOOL.
First, general results common to all the models are established. Then, the differences due to the selection
of particular delay kernels are considered. In particular, the differences in regions of stability
of the coexistence equilibrium are investigated. Finally, the effects on the predicted range of dynamics
between the classical Gause-type and the chemostat predator-prey models
are compared. / Thesis / Doctor of Philosophy (PhD)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/18699 |
| Date | January 2016 |
| Creators | Teslya, Alexandra |
| Contributors | Wolkowicz, Gail S.K., Mathematics and Statistics |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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