Understanding a Population Model for Mussel-Algae Interaction

Understanding a Population Model for Mussel-Algae Interaction

Bibliographic Details
Main Author: Vorpe, Katherine
Language:English
Published: Wittenberg University Honors Theses / OhioLINK 2020
Subjects:
Mathematics
Ecology
Applied Mathematics
Aquatic Sciences
nonlinear theories
nonlinear dynamics
numerical analysis
Geometric Singular Perturbation Theory
Invariant Manifold Theory
mussels
mussel beds
traveling waves
Online Access:http://rave.ohiolink.edu/etdc/view?acc_num=wuhonors1617970789779916
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spelling ndltd-OhioLink-oai-etd.ohiolink.edu-wuhonors16179707897799162021-08-03T07:17:00Z Understanding a Population Model for Mussel-Algae Interaction Vorpe, Katherine Mathematics Ecology Applied Mathematics Aquatic Sciences nonlinear theories nonlinear dynamics numerical analysis Geometric Singular Perturbation Theory Invariant Manifold Theory mussels mussel beds traveling waves 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. 2020 English text Wittenberg University Honors Theses / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=wuhonors1617970789779916 http://rave.ohiolink.edu/etdc/view?acc_num=wuhonors1617970789779916 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.
collection NDLTD
language English
sources NDLTD
topic Mathematics
Ecology
Applied Mathematics
Aquatic Sciences
nonlinear theories
nonlinear dynamics
numerical analysis
Geometric Singular Perturbation Theory
Invariant Manifold Theory
mussels
mussel beds
traveling waves
spellingShingle Mathematics
Ecology
Applied Mathematics
Aquatic Sciences
nonlinear theories
nonlinear dynamics
numerical analysis
Geometric Singular Perturbation Theory
Invariant Manifold Theory
mussels
mussel beds
traveling waves
Vorpe, Katherine
Understanding a Population Model for Mussel-Algae Interaction
author Vorpe, Katherine
author_facet Vorpe, Katherine
author_sort Vorpe, Katherine
title Understanding a Population Model for Mussel-Algae Interaction
title_short Understanding a Population Model for Mussel-Algae Interaction
title_full Understanding a Population Model for Mussel-Algae Interaction
title_fullStr Understanding a Population Model for Mussel-Algae Interaction
title_full_unstemmed Understanding a Population Model for Mussel-Algae Interaction
title_sort understanding a population model for mussel-algae interaction
publisher Wittenberg University Honors Theses / OhioLINK
publishDate 2020
url http://rave.ohiolink.edu/etdc/view?acc_num=wuhonors1617970789779916
work_keys_str_mv AT vorpekatherine understandingapopulationmodelformusselalgaeinteraction
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