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Bifurcation Analysis of Three-Strategy Imitative Dynamics with Mutations

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  • 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
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    References listed on IDEAS

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    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).

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