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The dynamics of a business game: A 2D-piecewise smooth nonlinear map

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  • Askar, S.S.
  • Al-khedhairi, A.

Abstract

In this paper, we give a proper investigation of the problem of remanufacturing duopoly game.11In [Physica A 514 (2019) 658-670] the authors have introduced the problem of remanufacturing duopoly game. The analytical and numerical analysis are wrong. They had to study their system as a piecewise one as shown in the current paper. A smooth piecewise map is introduced to describe such game. A rich analysis either analytical or numerical is presented in this paper in order to investigate the stability of the fixed points of the game’s model. Our obtained results show that those fixed points lose its stability due to flip and Neimark-Sacker border bifurcations. Furthermore, we study the stability of those points when there are periodic cycles with points jump from region to other region.

Suggested Citation

  • Askar, S.S. & Al-khedhairi, A., 2020. "The dynamics of a business game: A 2D-piecewise smooth nonlinear map," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    • Handle: RePEc:eee:phsmap:v:537:y:2020:i:c:s0378437119315717
    DOI: 10.1016/j.physa.2019.122766
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    Cited by:

    1. S. S. Askar & A. Al-khedhairi, 2019. "Cournot Duopoly Games: Models and Investigations," Mathematics, MDPI, vol. 7(11), pages 1-15, November.
    2. Liu, Cui & He, Rui-chun & Zhou, Wei & Li, Hui, 2021. "Dynamic analysis of airline bidding game based on nonlinear cost," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    3. Zhu, Yan-lan & Zhou, Wei & Chu, Tong, 2022. "Analysis of complex dynamical behavior in a mixed duopoly model with heterogeneous goods," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    4. Sameh S. Askar, 2020. "The Influences of Asymmetric Market Information on the Dynamics of Duopoly Game," Mathematics, MDPI, vol. 8(7), pages 1-12, July.

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