Mathematical models in evolutionary dynamics

Galiardi, Meghan Anne

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https://hdl.handle.net/2142/90535 Copy

Description

Title

Mathematical models in evolutionary dynamics

Author(s)

Galiardi, Meghan Anne

Issue Date

2016-04-14

Director of Research (if dissertation) or Advisor (if thesis)

DeVille, Lee

Doctoral Committee Chair(s)

Rapti, Zoi

Committee Member(s)

• Zharnitsky, Vadim
• Song, Renming

Department of Study

Mathematics

Discipline

Mathematics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(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.

Graduation Semester

2016-05

Type of Resource

text

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

Copyright and License Information

Copyright 2016 by Meghan Galiardi. All rights reserved.

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