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DeVille, Lee Rapti, Zoi Zharnitsky, Vadim Song, Renming Galiardi, Meghan Anne 2016-07-07T19:53:51Z 2016-07-07T19:53:51Z 2016-04-14 2016-05 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. Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2016-07-07 without embargo terms The student, Meghan Galiardi, accepted the attached license on 2016-04-13 at 17:26. The student, Meghan Galiardi, submitted this Dissertation for approval on 2016-04-13 at 22:32. This Dissertation was approved for publication on 2016-04-14 at 16:36. DSpace SAF Submission Ingestion Package generated from Vireo submission #9214 on 2016-07-07 at 13:30:37 Made available in DSpace on 2016-07-07T19:53:51Z (GMT). No. of bitstreams: 18 GALIARDI-DISSERTATION-2016.pdf: 5992618 bytes, checksum: 6a6e271330f52e6bfa6f709e18e1b225 (MD5) Algorithms.tex: 22299 bytes, checksum: ea989d97d3554fa63feb9b4d534f35a7 (MD5) CompetitiveExclusion.tex: 60040 bytes, checksum: 6bb46030105291c28cc250483aa9b9bd (MD5) Conclusions.tex: 1312 bytes, checksum: 3ee2ff683a3c22a57775f307b53ba96f (MD5) DeterministicAppendix.tex: 6072 bytes, checksum: 840becc8b69bdd78bf32d0d590007342 (MD5) Galiardi.bib: 29155 bytes, checksum: db9b24caee71a82d77ec11523b7b88d7 (MD5) Galiardi_Meghan.tex: 8152 bytes, checksum: ad29bafc9c8a46362a6f22321e2460c4 (MD5) Gardiner3Appendix.tex: 33350 bytes, checksum: 6978db30694f19d81c1a05b3fe872344 (MD5) Gardiner4Appendix.tex: 21949 bytes, checksum: e217c90e318fcc6bdce0ccd053a5663f (MD5) Gardiner5Appendix.tex: 32327 bytes, checksum: d4cacc864719b3752b7ecb684da0c11d (MD5) Gardiner7Appendix.tex: 34327 bytes, checksum: a873a132e4b836786ac4fb1fa3817450 (MD5) Intro.tex: 26811 bytes, checksum: 027a0bd3ea0c74816e14015cd78015df (MD5) MultipleStrategies.tex: 31421 bytes, checksum: 30423c2ec81893d9d2523a9c9db25daf (MD5) WKBAppendix.tex: 22253 bytes, checksum: b5198873cc58af9bc4a133a7b8631b0f (MD5) egt1.tex: 68080 bytes, checksum: 89f06736535fdb294374f6fef5f14078 (MD5) pictures.zip: 3660383 bytes, checksum: fbe6b89cb61e49e1314a579df3e275f1 (MD5) LICENSE.txt: 4212 bytes, checksum: e9d121984ed4cf801c2f50428d213316 (MD5) PROQUEST_LICENSE.txt: 4558 bytes, checksum: 3620868d81b13c3507e7a995309898da (MD5) Previous issue date: 2016-04-14 application/pdf http://hdl.handle.net/2142/90535 en Copyright 2016 by Meghan Galiardi. All rights reserved. evolutionary dynamics iterated Prisoner's dilemma competitive exclusion Markov process stochastic process mean-field limit switching times Mathematical models in evolutionary dynamics text text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.