Date on Master's Thesis/Doctoral Dissertation


Document Type

Doctoral Dissertation

Degree Name

Ph. D.



Degree Program

Applied and Industrial Mathematics, PhD

Committee Chair

Li, Bingtuan

Committee Co-Chair (if applicable)

Emery, Sarah

Committee Member

Emery, Sarah

Committee Member

Gie, Gung-Min

Committee Member

Hu, Changbing

Committee Member

Swanson, David

Author's Keywords

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.