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Complex dynamics analysis for a remanufacturing duopoly model with nonlinear cost

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Listed:
  • Peng, Yu
  • Lu, Qian
  • Xiao, Yue
  • Wu, Xue

Abstract

In this paper, a duopoly remanufacturing game of competition on output based on boundedly rational expectation is formulated. It involves an original equipment manufacturer (OEM) who makes new products and a third-party independent remanufacture (IR) who uses returned cores to produce differentiated products. Both parties adopt nonlinear cost functions. The study shows that consumer’s willingness-to-pay (WTP) has distinct effects on the OEM’s performance and the stability of Nash equilibrium. We present results on existence, stability and local bifurcations of the equilibrium points. Numerical simulations demonstrate that the system with varying model parameters may be driven to chaos and the loss of stability may be caused by period doubling bifurcations. It is also shown that the state variables feedback and parameter variation method can be used to keep the system from instability and chaos.

Suggested Citation

  • Peng, Yu & Lu, Qian & Xiao, Yue & Wu, Xue, 2019. "Complex dynamics analysis for a remanufacturing duopoly model with nonlinear cost," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 658-670.
    • Handle: RePEc:eee:phsmap:v:514:y:2019:i:c:p:658-670
    DOI: 10.1016/j.physa.2018.09.143
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    References listed on IDEAS

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    3. Askar, S.S. & Al-khedhairi, A., 2020. "On complex dynamic investigations of a piecewise smooth nonlinear duopoly game," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
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    5. Yang, Xuenan & Peng, Yu & Xiao, Yue & Wu, Xue, 2019. "Nonlinear dynamics of a duopoly Stackelberg game with marginal costs," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 185-191.
    6. Garmani, Hamid & Ait Omar, Driss & El Amrani, Mohamed & Baslam, Mohamed & Jourhmane, Mostafa, 2020. "Analysis of a dynamics duopoly game with two content providers," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
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    8. Hussain, Jafar & Lee, Chien-Chiang & Hu, Danting, 2023. "Maximizing load capacity factor through a carbon-neutral environment via a simulation of carbon peak," Economic Analysis and Policy, Elsevier, vol. 79(C), pages 746-764.
    9. Tian, Baodan & Zhang, Yong & Li, Jiamei, 2020. "Stochastic perturbations for a duopoly Stackelberg model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    10. Xi, Xuan & Zhang, Yulin, 2021. "Complexity analysis of production, fertilizer-saving level, and emission reduction efforts decisions in a two-parallel agricultural product supply chain," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    11. Sameh Askar, 2021. "Complex Investigations of a Piecewise-Smooth Remanufacturing Bertrand Duopoly Game," Mathematics, MDPI, vol. 9(20), pages 1-13, October.
    12. Sameh S Askar & Abdulrahman Al-Khedhairi, 2020. "Local and Global Dynamics of a Constraint Profit Maximization for Bischi–Naimzada Competition Duopoly Game," Mathematics, MDPI, vol. 8(9), pages 1-16, August.
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    14. Peng, Yu & Xiao, Yue & Lu, Qian & Wu, Xue & Zhao, Yueru, 2020. "Chaotic dynamics in Cournot duopoly model with bounded rationality based on relative profit delegation maximization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).

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