Date on Master's Thesis/Doctoral Dissertation
Applied and Industrial Mathematics, PhD
Committee Co-Chair (if applicable)
Overcompensation; reaction-diffusion equation; spreading speed
We consider both the nonspatial model and spatial model of a species that gives birth to eggs at the end of the year. It is assumed that the timing of emergence from eggs is controled by phenology, which is density dependent. In general, the solution maps for our models are implicit; When the solution map is explicit, it is extremely complex and it is easier to work with the implicit map. We derive integral conditions for which the nonspatial model exhibits strong Allee effect. We also provide a necessary condition and a sufficient condition for the existence of positive equilibrium solutions. We also numerically explore the complex dynamics of both models. It is shown that varying a parameter can cause an Allee threshold to appear/disappear. We also show that the spatial model can have a growth function with overcompensation, wave solutions, oscillating waves, and nonspreading solutions. It is also shown that the wave solutions can have constant, oscillating, or chaotic spreading speeds. We also provide an example where the solutions to the spatial model are persistent, even though the underlying dynamics of the nonspatial model is essential extinction.
Pervenecki, Timothy James, "Allee effects introduced by density dependent phenology." (2019). Electronic Theses and Dissertations. Paper 3291.