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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.","abstract_html":"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.","abstract_has_math":false,"creators":["Galiardi, Meghan Anne"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["DeVille, Lee","Rapti, Zoi","Zharnitsky, Vadim","Song, Renming"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-07-07T19:53:51Z","date_published":"2016-07-07T19:53:51Z","updated_at":"2026-07-22T22:26:32Z","subjects":["evolutionary dynamics","iterated Prisoner's dilemma","competitive exclusion","Markov process","stochastic process","mean-field limit","switching times"],"languages":["en"],"rights":["Copyright 2016 by Meghan Galiardi. 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