Evolutionary Stable Strategies and Cubic Vector Fields
Dynamical Systems
2024-05-08 v3
Abstract
The introduction of concepts of Game Theory and Ordinary Differential Equations into Biology gave birth to the field of Evolutionary Stable Strategies, with applications in Biology, Genetics, Politics, Economics and others. In special, the model composed by two players having two pure strategies each results in a planar cubic vector field with an invariant octothorpe. Therefore, in this paper we study such class of vector fields, suggesting the notion of genericity and providing the global phase portraits of the generic systems with a singularity at the central region of the octothorpe.
Keywords
Cite
@article{arxiv.2208.11694,
title = {Evolutionary Stable Strategies and Cubic Vector Fields},
author = {Jefferson Bastos and Claudio Buzzi and Paulo Santana},
journal= {arXiv preprint arXiv:2208.11694},
year = {2024}
}