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Stability analysis of game models with fixed and stochastic delays

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  • Hu, Limi
  • Qiu, Xiaoling

Abstract

In this paper, we combine evolutionary game with dynamics, and discuss two kinds of game models with time delay. First, based on continuous distributed (kernel function) stochastic delay, we give the asymptotic stability condition of general three-strategy game model. Second, we study the replicator dynamics of two-community three-strategy game model with two fixed time delays (i.e. τ1 within the community and τ2 between different communities). Based on Hopf bifurcation theory, by calculating the critical conditions for the existence of bifurcation, the influence of bifurcation on the stability of equilibrium points is analyzed. Finally, we take rock-paper-scissors game as an example to verify the correctness of the theoretical results, when the delay τ meets certain conditions or doesn’t exceed the critical value, the stability of the system will not change.

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  • Hu, Limi & Qiu, Xiaoling, 2022. "Stability analysis of game models with fixed and stochastic delays," Applied Mathematics and Computation, Elsevier, vol. 435(C).
    • Handle: RePEc:eee:apmaco:v:435:y:2022:i:c:s0096300322005471
    DOI: 10.1016/j.amc.2022.127473
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    References listed on IDEAS

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    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. Zhang, Zizhen & Kundu, Soumen & Tripathi, Jai Prakash & Bugalia, Sarita, 2020. "Stability and Hopf bifurcation analysis of an SVEIR epidemic model with vaccination and multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    5. Nesrine Ben-Khalifa & Rachid El-Azouzi & Yezekael Hayel, 2018. "Discrete and Continuous Distributed Delays in Replicator Dynamics," Dynamic Games and Applications, Springer, vol. 8(4), pages 713-732, December.
    6. Xiaojie Chen & Attila Szolnoki, 2018. "Punishment and inspection for governing the commons in a feedback-evolving game," PLOS Computational Biology, Public Library of Science, vol. 14(7), pages 1-15, July.
    7. Wettergren, Thomas A., 2021. "Replicator dynamics of an N-player snowdrift game with delayed payoffs," Applied Mathematics and Computation, Elsevier, vol. 404(C).
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    Cited by:

    1. Wettergren, Thomas A., 2023. "Replicator dynamics of evolutionary games with different delays on costs and benefits," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    2. Xiuling Li & Haotian Fan, 2024. "Bifurcation Analysis of a Class of Two-Delay Lotka–Volterra Predation Models with Coefficient-Dependent Delay," Mathematics, MDPI, vol. 12(10), pages 1-22, May.
    3. Tianjun Su & Linhai Wu & Jingxiang Zhang, 2024. "Evolutionary Game and Simulation Analysis of Food Safety Regulation under Time Delay Effect," Mathematics, MDPI, vol. 12(8), pages 1-23, April.
    4. Mengzhu Xu & Zixin Liu & Changjin Xu & Nengfa Wang, 2024. "Evolutionary Game Analysis of Digital Financial Enterprises and Regulators Based on Delayed Replication Dynamic Equation," Mathematics, MDPI, vol. 12(3), pages 1-18, January.

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