Bifurcation analysis of three-strategy imitative dynamics with mutations
type: Item
instance of: scholarly article
title: Bifurcation analysis of three-strategy imitative dynamics with mutations
zbMATH Open document ID: 1429.34072
DOI: 10.1155/2019/4134105
author: Wenjun Hu
author: Haiyan Tian
author: Gang Zhang
published in: Complexity
publication date: 2019-11-25T00:00:00Z
review text: Summary: Evolutionary game dynamics is an important research, which is widely used in many fields such as social networks, biological systems, and cooperative behaviors. This paper focuses on the Hopf bifurcation in imitative dynamics of three strategies (Rock-Paper-Scissors) with mutations. First, we verify that there is a Hopf bifurcation in the imitative dynamics with no mutation. Then, we find that there is a critical value of mutation such that the system tends to an unstable limit cycle created in a subcritical Hopf bifurcation. Moreover, the Hopf bifurcation exists for other kinds of the considered mutation patterns. Finally, the theoretical results are verified by numerical simulations through Rock-Paper-Scissors game.
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 91A22
Mathematics Subject Classification ID: 37N40
zbMATH DE Number: 7136318
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2019/4134105
OpenAlex ID: W2982467503
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description: scientific article; zbMATH DE number 7136318