Date on Master's Thesis/Doctoral Dissertation
Applied and Industrial Mathematics, PhD
mathematical biology; integrodifference equation; Allee effect; overcompensation; spatial population ecology
Previous work in Integro-Difference models have generally considered Allee effects and over-compensation separately, and have either focused on bounded domain problems or asymptotic spreading results. Some recent results by Sullivan et al. (2017 PNAS 114(19), 5053-5058) combining Allee and over-compensation in an Integro-Difference framework have shown chaotic fluctuating spreading speeds. In this thesis, using a tractable parameterized growth function, we analytically demonstrate that when Allee and over-compensation are present solutions which persist but essentially remain in a compact domain exist. We investigate the stability of these solutions numerically. We also numerically demonstrate the existence of such solutions for more general growth functions.
Otto, Garrett Luther, "Nonspreading solutions in integro-difference models with allee and overcompensation effects." (2017). Electronic Theses and Dissertations. Paper 2858.
Retrieved from https://ir.library.louisville.edu/etd/2858