Hopf Bifurcations in Replicator Dynamics with Distributed Delays
Systems and Control
2017-03-21 v1
Abstract
In this paper, we study the existence and the property of the Hopf bifurcation in the two-strategy replicator dynamics with distributed delays. In evolutionary games, we assume that a strategy would take an uncertain time delay to have a consequence on the fitness (or utility) of the players. As the mean delay increases, a change in the stability of the equilibrium (Hopf bifurcation) may occur at which a periodic oscillation appears. We consider Dirac, uniform, Gamma, and discrete delay distributions, and we use the Poincar\'e- Lindstedt's perturbation method to analyze the Hopf bifurcation. Our theoretical results are corroborated with numerical simulations.
Cite
@article{arxiv.1703.06721,
title = {Hopf Bifurcations in Replicator Dynamics with Distributed Delays},
author = {Nesrine Ben Khalifa and Rachid El Azouzi and Yezekael Hayel},
journal= {arXiv preprint arXiv:1703.06721},
year = {2017}
}