Date on Master's Thesis/Doctoral Dissertation
12-2015
Document Type
Doctoral Dissertation
Degree Name
Ph. D.
Department
Mathematics
Degree Program
Applied and Industrial Mathematics, PhD
Committee Chair
Li, Bingtuan
Committee Co-Chair (if applicable)
Li, Jiaxu
Committee Member
Li, Jiaxu
Committee Member
Gill, Ryan
Committee Member
Hu, Changbing
Committee Member
Song, Wei
Author's Keywords
allee effect; invasion; spreading speed; traveling wave; two-sex population model
Abstract
Virtually every ecosystem has been invaded by exotic organisms with potentially drastic consequences for the native fauna or flora. Studying the forms and rates of invading species has been an important topic in spatial ecology. We investigate two two-species competition models with Allee effects in the forms of reaction-diffusion equations and integro-difference equations. We discuss the spatial transitions from a mono-culture equilibrium to a coexistence equilibrium or a different mono-culture equilibrium in these models. We provide formulas for the spreading speeds based on the linear determinacy and show the results on the existence of traveling waves. We also study a two-sex stage-structured model. We carry out initial analysis for the spreading speed and conduct numerical simulations on the traveling waves and spreading speeds in the two-sex model.
Recommended Citation
Meng, Quancheng, "Spreading speeds and traveling waves in some population models." (2015). Electronic Theses and Dissertations. Paper 2297.
https://doi.org/10.18297/etd/2297
