Mathematical models in evolutionary dynamics

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2016

Author dc:creator

• Galiardi, Meghan Anne

Contributors dc:contributor

• DeVille, Lee
• Rapti, Zoi
• Zharnitsky, Vadim
• Song, Renming

• evolutionary dynamics
• iterated Prisoner's dilemma
• competitive exclusion
• Markov process
• stochastic process
• mean-field limit
• switching times

Statement dc:rights

• Copyright 2016 by Meghan Galiardi. All rights reserved.

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/90535

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/90535