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Dynamical analysis and chaos control in a heterogeneous Kopel duopoly game

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  • A. A. Elsadany

    (Suez Canal University)

  • A. M. Awad

    (Suez Canal University)

Abstract

A dynamic of a nonlinear Kopel duopoly game with heterogeneous players is presented. By assuming two heterogeneous players where one player use naive expectation whereas the other employs a technique of adaptive. The stability conditions of equilibrium points are analyzed. Numerical simulations are used to show bifurcation diagrams, phase portraits and sensitive dependence on initial conditions. The chaotic behavior of the game has been controlled by using feedback control method.

Suggested Citation

  • A. A. Elsadany & A. M. Awad, 2016. "Dynamical analysis and chaos control in a heterogeneous Kopel duopoly game," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(4), pages 617-639, December.
    • Handle: RePEc:spr:indpam:v:47:y:2016:i:4:d:10.1007_s13226-016-0206-3
    DOI: 10.1007/s13226-016-0206-3
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    References listed on IDEAS

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    Cited by:

    1. Long, Jianjun & Wang, Fenglian, 2024. "Complexity of a two-stage R&D game within a cluster supply chain considering vertical R&D spillovers, effective information, and government subsidies," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 606-621.
    2. Xiaoliang Li & Kongyan Chen, 2023. "Equilibria and their stability in an asymmetric duopoly model of Kopel," Papers 2301.12628, arXiv.org.
    3. Li Cheng & Liu Conglin, 2023. "Game analysis and pricing strategy of duopoly airlines based on service," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 14(3), pages 1103-1124, June.
    4. Li, Bo & Liang, Houjun & Shi, Lian & He, Qizhi, 2022. "Complex dynamics of Kopel model with nonsymmetric response between oligopolists," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).

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