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 Member

Emery, Sarah

Committee Member

Hu, Changbing

Committee Member

Li, Jiaxu

Author's Keywords

reaction-diffusion; allee effect; protection zone


A protection zone model represents a patchy environment with positive growth over the protection zone and strong Allee effect growth outside the protection zone. Generally, these models are considered through the corresponding eigenvalue problem, but that has certain limitations. In this thesis, a general protection zone model is considered. This model makes no assumption on the direction of the traveling wave solution over the Strong Allee effect patch. We use phase portrait analysis of this protection zone model to draw conclusions about the existence of equilibrium solutions. We establish the existence of three types of equilibrium solutions and the necessary conditions for each to exist. Then, through numerical techniques, we further explore the existence and behavior of these equilibrium solutions.