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Description
Title: | Mathematical models in evolutionary dynamics |
Author(s): | Galiardi, Meghan Anne |
Director of Research: | DeVille, Lee |
Doctoral Committee Chair(s): | Rapti, Zoi |
Doctoral Committee Member(s): | Zharnitsky, Vadim; Song, Renming |
Department / Program: | Mathematics |
Discipline: | Mathematics |
Degree Granting Institution: | University of Illinois at Urbana-Champaign |
Degree: | Ph.D. |
Genre: | Dissertation |
Subject(s): | evolutionary dynamics
iterated Prisoner's dilemma competitive exclusion Markov process stochastic process mean-field limit switching times |
Abstract: | We consider two mathematical models in evolutionary dynamics. The first model is an extension of an evolutionary game theory model proposed by Martin Nowak. We consider both a mean field deterministic approach and a weak noise stochastic approach, but the focus is on latter which is an uncommon approach for this type of model. The second model is an extension of a competitive exclusion model studied by DeVille et. al. We again consider both a mean field deterministic approach and a weak noise stochastic approach, this time with the focus on the former where we are able to prove numerous global stability results. |
Issue Date: | 2016-04-14 |
Type: | Text |
URI: | http://hdl.handle.net/2142/90535 |
Rights Information: | Copyright 2016 by Meghan Galiardi. All rights reserved. |
Date Available in IDEALS: | 2016-07-07 |
Date Deposited: | 2016-05 |
This item appears in the following Collection(s)
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Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois