Date on Master's Thesis/Doctoral Dissertation
8-2024
Document Type
Master's Thesis
Degree Name
M.A.
Department
Mathematics
Degree Program
Mathematics, MA
Committee Chair
Li, Bingtuan
Committee Co-Chair (if applicable)
Swanson, David
Committee Member
Swanson, David
Committee Member
Song, Wei
Abstract
We consider a reaction-diffusion equation that models a population in a shifting bounded habitat with a protection zone and the Allee effect. We assume that the population growth function exhibits the strong Allee effect and has a positive integral within the protection zone (indicating population persistence) and a negative integral in the surrounding patches (indicating population decay). We prove that the existence of steady-state solutions to this system depends on the length of the protection zone. It is demonstrated that there exists some value H* such that, for a protection zone of size H*, there exists a solution and, for a larger protection zone, there exists more than one solution. For smaller protection zones, we prove there exists no solution. We then examine the case study of a steady-state solution through simulation.
Recommended Citation
Henderson, Davis, "Effects of a protection zone in a reaction-diffusion model with shifting bounded habitat and Allee effect." (2024). Electronic Theses and Dissertations. Paper 4457.
Retrieved from https://ir.library.louisville.edu/etd/4457
Included in
Dynamic Systems Commons, Ordinary Differential Equations and Applied Dynamics Commons, Population Biology Commons
