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The stability of imitation dynamics with discrete distributed delays

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  • Hu, Wenjun
  • Zhang, Gang
  • Tian, Haiyan

Abstract

This paper investigates the stability in a new model of imitation dynamics with discrete distributed delays. Some sufficient conditions of the asymptotical stability for the interior Nash equilibrium of the imitation dynamics with multiple-delay are obtained. Finally, numerical experiments are displayed which support the theoretical results through the Snowdrift game.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:521:y:2019:i:c:p:218-224
    DOI: 10.1016/j.physa.2019.01.045
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    References listed on IDEAS

    as
    1. Wang, Xianjia & Lv, Shaojie & Quan, Ji, 2017. "The evolution of cooperation in the Prisoner’s Dilemma and the Snowdrift game based on Particle Swarm Optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 286-295.
    2. Yang, Zhihu & Li, Zhi & Wu, Te & Wang, Long, 2014. "Effects of payoff-related velocity in the co-evolutionary snowdrift game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 304-311.
    3. Elizabeth Wesson & Richard Rand, 2016. "Hopf Bifurcations in Delayed Rock–Paper–Scissors Replicator Dynamics," Dynamic Games and Applications, Springer, vol. 6(1), pages 139-156, March.
    4. Shu, Feng & Liu, Xingwen & Fang, Kai & Chen, Hao, 2018. "Memory-based snowdrift game on a square lattice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 15-26.
    5. Ye, Wenxing & Fan, Suohai, 2017. "Evolutionary snowdrift game with rational selection based on radical evaluation," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 310-317.
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    Cited by:

    1. Jinxiu Pi & Hui Yang & Yadong Shu & Chongyi Zhong & Guanghui Yang, 2020. "The Stability of Two-Community Replicator Dynamics with Discrete Multi-Delays," Mathematics, MDPI, vol. 8(12), pages 1-17, November.
    2. Wenjun Hu & Haiyan Tian & Gang Zhang, 2019. "Bifurcation Analysis of Three-Strategy Imitative Dynamics with Mutations," Complexity, Hindawi, vol. 2019, pages 1-8, October.
    3. Wang, Si-Yi & Feng, Tian-Jiao & Tao, Yi & Wu, Jia-Jia, 2023. "Impact of individual sensitivity to payoff difference between individuals on a discrete-time imitation dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    4. 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).

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