Bifurcation Analysis of Three-Strategy Imitative Dynamics with Mutations

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...

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Main Authors: Wenjun Hu, Haiyan Tian, Gang Zhang
Format: Article
Language:English
Published: Wiley 2019-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2019/4134105
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author Wenjun Hu
Haiyan Tian
Gang Zhang
author_facet Wenjun Hu
Haiyan Tian
Gang Zhang
author_sort Wenjun Hu
collection DOAJ
description 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.
format Article
id doaj-art-a2bfb87c467a478ab2ce1fda104a991a
institution Kabale University
issn 1076-2787
1099-0526
language English
publishDate 2019-01-01
publisher Wiley
record_format Article
series Complexity
spelling doaj-art-a2bfb87c467a478ab2ce1fda104a991a2025-02-03T06:01:00ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/41341054134105Bifurcation Analysis of Three-Strategy Imitative Dynamics with MutationsWenjun Hu0Haiyan Tian1Gang Zhang2College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, ChinaCollege of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, ChinaCollege of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, ChinaEvolutionary 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.http://dx.doi.org/10.1155/2019/4134105
spellingShingle Wenjun Hu
Haiyan Tian
Gang Zhang
Bifurcation Analysis of Three-Strategy Imitative Dynamics with Mutations
Complexity
title Bifurcation Analysis of Three-Strategy Imitative Dynamics with Mutations
title_full Bifurcation Analysis of Three-Strategy Imitative Dynamics with Mutations
title_fullStr Bifurcation Analysis of Three-Strategy Imitative Dynamics with Mutations
title_full_unstemmed Bifurcation Analysis of Three-Strategy Imitative Dynamics with Mutations
title_short Bifurcation Analysis of Three-Strategy Imitative Dynamics with Mutations
title_sort bifurcation analysis of three strategy imitative dynamics with mutations
url http://dx.doi.org/10.1155/2019/4134105
work_keys_str_mv AT wenjunhu bifurcationanalysisofthreestrategyimitativedynamicswithmutations
AT haiyantian bifurcationanalysisofthreestrategyimitativedynamicswithmutations
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