Date on Master's Thesis/Doctoral Dissertation
12-2023
Document Type
Doctoral Dissertation
Degree Name
Ph. D.
Department
Mathematics
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
Abstract
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.
Recommended Citation
Johnson, Isaac, "Effects of a protection zone in a reaction-diffusion model with strong Allee effect." (2023). Electronic Theses and Dissertations. Paper 4216.
Retrieved from https://ir.library.louisville.edu/etd/4216
