Abstract

Predation and harvesting play critical roles in maintaining biodiversity in ecological communities. Too much harvesting may drive a species to extinction, while too little harvesting may allow a population to drive out competing species. The spatial features of a habitat can also significantly affect population dynamics within these communities. Here, we formulate and analyze three ordinary differential equation models for the population density of a single species. Each model differs in its assumptions about how the species is harvested. We then extend each of these models to analogous partial differential equation models that more explicitly describe the spatial habitat and the movement of individuals using reaction-diffusion equations. We study the existence and stability of non-zero equilibria of these models in terms of each model's parameters. Biological interpretations for these results are discussed.

Thesis Completion

2023

Semester

Spring

Thesis Chair/Advisor

Nevai, Andrew

Degree

Bachelor of Science (B.S.)

College

College of Sciences

Department

Mathematics

Degree Program

Mathematics

Language

English

Access Status

Open Access

Release Date

5-15-2023

Download

Included in

Mathematics Commons

Share

COinS
 

Accessibility Statement

This item was created or digitized prior to April 24, 2027, or is a reproduction of legacy media created before that date. It is preserved in its original, unmodified state specifically for research, reference, or historical recordkeeping. In accordance with the ADA Title II Final Rule, the University Libraries provides accessible versions of archival materials upon request. To request an accommodation for this item, please submit an accessibility request form.