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On the Dynamics of a Discrete Fractional-Order Cournot–Bertrand Competition Duopoly Game

Author

Listed:
  • Abdulrahman Al-Khedhairi
  • Abdelalim A. Elsadany
  • Amr Elsonbaty
  • Ali Ahmadian

Abstract

A discreet fractional-order Cournot–Bertrand competition duopoly game is introduced based on the fractional-order difference calculus of the Caputo operator. The model is designed when players can make long memory decisions. The local stability of equilibrium points is discussed for the proposed model. Some numerical simulations explore the model’s bifurcation and chaos by employing bifurcation diagrams, phase portraits, maximal Lyapunov exponents, and time series. According to our findings, the fractional-order parameter has an effect on the game’s stability and dynamics.

Suggested Citation

  • Abdulrahman Al-Khedhairi & Abdelalim A. Elsadany & Amr Elsonbaty & Ali Ahmadian, 2022. "On the Dynamics of a Discrete Fractional-Order Cournot–Bertrand Competition Duopoly Game," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-13, February.
    • Handle: RePEc:hin:jnlmpe:8249215
    DOI: 10.1155/2022/8249215
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    Cited by:

    1. Khalil S. Al-Basyouni & Elsayed M. Elsayed, 2023. "On Some Solvable Systems of Some Rational Difference Equations of Third Order," Mathematics, MDPI, vol. 11(4), pages 1-13, February.
    2. Hashem Althagafi & Ahmed Ghezal, 2024. "Analytical Study of Nonlinear Systems of Higher-Order Difference Equations: Solutions, Stability, and Numerical Simulations," Mathematics, MDPI, vol. 12(8), pages 1-20, April.
    3. Dalal Yahya Alzahrani & Fuaada Mohd Siam & Farah A. Abdullah, 2023. "Elucidating the Effects of Ionizing Radiation on Immune Cell Populations: A Mathematical Modeling Approach with Special Emphasis on Fractional Derivatives," Mathematics, MDPI, vol. 11(7), pages 1-21, April.

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