IDEAS home Printed from https://ideas.repec.org/a/hin/complx/4134105.html
   My bibliography  Save this article

Bifurcation Analysis of Three-Strategy Imitative Dynamics with Mutations

Author

Listed:
  • Wenjun Hu
  • Haiyan Tian
  • Gang Zhang

Abstract

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.

Suggested Citation

  • Wenjun Hu & Haiyan Tian & Gang Zhang, 2019. "Bifurcation Analysis of Three-Strategy Imitative Dynamics with Mutations," Complexity, Hindawi, vol. 2019, pages 1-8, October.
    • Handle: RePEc:hin:complx:4134105
    DOI: 10.1155/2019/4134105
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/8503/2019/4134105.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/8503/2019/4134105.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2019/4134105?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Xinhua Wang & Rongwu Lu & Hao Yu & Dan Li, 2019. "Stability of the Evolutionary Game System and Control Strategies of Behavior Instability in Coal Mine Safety Management," Complexity, Hindawi, vol. 2019, pages 1-14, February.
    2. Martin A. Nowak & Akira Sasaki & Christine Taylor & Drew Fudenberg, 2004. "Emergence of cooperation and evolutionary stability in finite populations," Nature, Nature, vol. 428(6983), pages 646-650, April.
    3. Rong Liu & Guirong Liu, 2018. "Asymptotic Behavior of a Stochastic Two-Species Competition Model under the Effect of Disease," Complexity, Hindawi, vol. 2018, pages 1-15, November.
    4. Kukla, Elżbieta & Płatkowski, Tadeusz, 2013. "Onset of limit cycles in population games with attractiveness driven strategy choice," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 77-82.
    5. Hommes, Cars H. & Ochea, Marius I., 2012. "Multiple equilibria and limit cycles in evolutionary games with Logit Dynamics," Games and Economic Behavior, Elsevier, vol. 74(1), pages 434-441.
    6. Cheung, Man-Wah, 2016. "Imitative dynamics for games with continuous strategy space," Games and Economic Behavior, Elsevier, vol. 99(C), pages 206-223.
    7. Rongwu Lu & Xinhua Wang & Hao Yu & Dan Li, 2018. "Multiparty Evolutionary Game Model in Coal Mine Safety Management and Its Application," Complexity, Hindawi, vol. 2018, pages 1-10, March.
    8. Junyuan Yang & Xiaoyan Wang, 2018. "Threshold Dynamics of an SIR Model with Nonlinear Incidence Rate and Age-Dependent Susceptibility," Complexity, Hindawi, vol. 2018, pages 1-15, October.
    9. Xu, Bin & Zhou, Hai-Jun & Wang, Zhijian, 2013. "Cycle frequency in standard Rock–Paper–Scissors games: Evidence from experimental economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 4997-5005.
    10. Platkowski, Tadeusz & Zakrzewski, Jan, 2011. "Asymptotically stable equilibrium and limit cycles in the Rock–Paper–Scissors game in a population of players with complex personalities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4219-4226.
    11. Hu, Wenjun & Zhang, Gang & Tian, Haiyan, 2019. "The stability of imitation dynamics with discrete distributed delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 218-224.
    12. Xu, Hedong & Fan, Suohai & Tian, Cunzhi & Xiao, Xinrong, 2019. "Evolutionary investor sharing game on networks," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 138-145.
    13. Yang, Han-Xin & Chen, Xiaojie, 2018. "Promoting cooperation by punishing minority," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 460-466.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kabir, K.M. Ariful & Tanimoto, Jun, 2021. "The role of pairwise nonlinear evolutionary dynamics in the rock–paper–scissors game with noise," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    2. Kubyana, Mmatlou S. & Landi, Pietro & Hui, Cang, 2024. "Adaptive rock-paper-scissors game enhances eco-evolutionary performance at cost of dynamic stability," Applied Mathematics and Computation, Elsevier, vol. 468(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Qin, Shipeng & Zhang, Gang & Tian, Haiyan & Hu, Wenjun & Zhang, Xiaoming, 2020. "Dynamics of asymmetric division of labor game with environmental feedback," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 543(C).
    2. Zhang, Boyu & An, Xinmiao & Dong, Yali, 2021. "Conditional cooperator enhances institutional punishment in public goods game," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    3. Huang, Shaoxu & Liu, Xuesong & Hu, Yuhan & Fu, Xiao, 2023. "The influence of aggressive behavior on cooperation evolution in social dilemma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    4. Huang, Xingjun & Lin, Yun & Lim, Ming K. & Zhou, Fuli & Liu, Feng, 2022. "Electric vehicle charging station diffusion: An agent-based evolutionary game model in complex networks," Energy, Elsevier, vol. 257(C).
    5. Wang, Mie & Kang, HongWei & Shen, Yong & Sun, XingPing & Chen, QingYi, 2021. "The role of alliance cooperation in spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    6. Song, Fanpeng & Wu, Jianliang & Fan, Suohai & Jing, Fei, 2020. "Transcendental behavior and disturbance behavior favor human development," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    7. Chen, Qiao & Chen, Tong & Wang, Yongjie, 2019. "Cleverly handling the donation information can promote cooperation in public goods game," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 363-373.
    8. Umezuki, Yosuke, 2018. "Bifurcation analysis of the rock–paper–scissors game with discrete-time logit dynamics," Mathematical Social Sciences, Elsevier, vol. 95(C), pages 54-65.
    9. Li, Bin-Quan & Wu, Zhi-Xi & Guan, Jian-Yue, 2022. "Critical thresholds of benefit distribution in an extended snowdrift game model," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    10. Zhijian Wang & Yanran Zhou & Jaimie W. Lien & Jie Zheng & Bin Xu, 2016. "Extortion Can Outperform Generosity in the Iterated Prisoners' Dilemma," Levine's Bibliography 786969000000001297, UCLA Department of Economics.
    11. Kukla, Elżbieta & Płatkowski, Tadeusz, 2013. "Onset of limit cycles in population games with attractiveness driven strategy choice," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 77-82.
    12. Ye, Wenxing & Fan, Suohai, 2020. "Evolutionary traveler’s dilemma game based on particle swarm optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).
    13. Liu, Jinzhuo & Meng, Haoran & Wang, Wei & Li, Tong & Yu, Yong, 2018. "Synergy punishment promotes cooperation in spatial public good game," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 214-218.
    14. Xin, Baogui & Peng, Wei & Kwon, Yekyung, 2020. "A discrete fractional-order Cournot duopoly game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
    15. repec:cla:levarc:786969000000001297 is not listed on IDEAS
    16. Mahdi Hajihashemi & Keivan Aghababaei Samani, 2022. "Multi-strategy evolutionary games: A Markov chain approach," PLOS ONE, Public Library of Science, vol. 17(2), pages 1-17, February.
    17. Zhang, Wei & Brandes, Ulrik, 2023. "Is cooperation sustained under increased mixing in evolutionary public goods games on networks?," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    18. Chen, Yunong & Belmonte, Andrew & Griffin, Christopher, 2021. "Imitation of success leads to cost of living mediated fairness in the Ultimatum Game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    19. Sergio Currarini & Carmen Marchiori & Alessandro Tavoni, 2016. "Network Economics and the Environment: Insights and Perspectives," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 65(1), pages 159-189, September.
    20. Christian Hilbe & Moshe Hoffman & Martin A. Nowak, 2015. "Cooperate without Looking in a Non-Repeated Game," Games, MDPI, vol. 6(4), pages 1-15, September.
    21. Takuya Sekiguchi, 2023. "Fixation Probabilities of Strategies for Trimatrix Games and Their Applications to Triadic Conflict," Dynamic Games and Applications, Springer, vol. 13(3), pages 1005-1033, September.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hin:complx:4134105. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.