Nonspreading solutions in integro-difference models with allee and overcompensation effects.

mathematical biology;integrodifference equation;Allee effect;overcompensation;spatial population ecology

Garrett Luther Otto

University:University of Louisville

Department:Mathematics

关键词: mathematical biology;    integrodifference equation;    Allee effect;    overcompensation;    spatial population ecology;   

Others  :  https://ir.library.louisville.edu/cgi/viewcontent.cgi?article=3970&context=etd

美国|英语

来源: The Universite of Louisville's Institutional Repository

【 摘 要 】

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.