Mathematical models in evolutionary dynamics

evolutionary dynamics;"iterated Prisoners dilemma";competitive exclusion;Markov process;stochastic process;mean-field limit;switching times

Galiardi, Meghan Anne

关键词: evolutionary dynamics;    "iterated Prisoners dilemma";    competitive exclusion;    Markov process;    stochastic process;    mean-field limit;    switching times;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/90535/GALIARDI-DISSERTATION-2016.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

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.