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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:Thesis
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


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