|Title||Perturbation in replicator equation to study discrete time evolutionary population|
|Presenter||Geetika Verma (University of South Australia)|
|Session||Analysis and Partial Differential Equations|
The replicator equation is used to understand the dynamic evolution of populations in both continuous time and discrete time. In this talk we consider a simple model with two species and use the replicator equation to study discrete time evolution of the population in the presence of small random or deterministic perturbations to each generation caused either by genetic mutation or migration. Our most important observation is that for small perturbations the model contains two important capture regions that ensure stability of the iterated map describing the evolution but that for larger perturbations one or both of these regions may disappear. Our future research will try to extend our analysis to more complex models.
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