Honors Thesis Archive

Author	Katherine Vorpe
Title	Understanding a Population Model for Mussel-Algae Interaction
Department	Mathematics
Advisors	Adam Parker, Alyssa Hoofnagle, and Jeremiah Williams
Year	2020
Honors	University Honors
Full Text	View Thesis (2495 KB)
Abstract	The objective of this thesis is to understand the systematic analytic treatment of the model presented in Anna Ghazaryan and Vahagn Manukian's journal article, “Coherent Structures in a Population Model for Mussel-Algae Interaction," which concentrates on the formation of mussel beds on soft sediments, like those found on cobble beaches. The study will investigate how the tidal flow of the water is the main structure that creates the mussel-algae interaction observed on soft sediments. With this investigation, the idea of fast-time and slow-time systems is explicated according to Geometric Singular Perturbation Theory, how Invariant Manifold Theory proves the existence of our solutions, the process of non-dimensionalization, and the re-scaling of the model. It will apply concepts found in nonlinear dynamics to discover equilibria and nullclines of the system. Finally, the study will discuss what the findings mean in context of the population model and the implications of tidal flow on other ecological relationships.