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<p>This study examines the dynamic behavior of a quantity-based Cournot duopoly game, emphasizing the interactions among stability, bifurcation, and chaos management. The presence and stability of fixed points are analytically investigated, and the Neimark-Sacker bifurcation at the positive fixed point is thoroughly addressed. A hybrid control method is used to stabilize chaotic dynamics, successfully postponing bifurcation and improving system predictability. The research is expanded to a networked context, whereby interconnected Cournot duopolies demonstrate the impact of coupling strength and network structure on system dynamics. Numerical simulations corroborate the theoretical findings, demonstrating transitions among stable, periodic, and chaotic processes. These findings offer valuable insights into the complexities of competitive markets and the role of control mechanisms in ensuring stability and efficiency.</p>

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Analytical and Numerical Exploration of Stability, Bifurcation, and Chaos Control in a Cournot Duopoly and Coupled Network Dynamics

  • 期刊论文

  • 发表日期：

    2025年8月3日

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  • Rizwan Ahmed,
  • Moataz Alosaimi,
  • Md. Jasim Uddin

摘要

This study examines the dynamic behavior of a quantity-based Cournot duopoly game, emphasizing the interactions among stability, bifurcation, and chaos management. The presence and stability of fixed points are analytically investigated, and the Neimark-Sacker bifurcation at the positive fixed point is thoroughly addressed. A hybrid control method is used to stabilize chaotic dynamics, successfully postponing bifurcation and improving system predictability. The research is expanded to a networked context, whereby interconnected Cournot duopolies demonstrate the impact of coupling strength and network structure on system dynamics. Numerical simulations corroborate the theoretical findings, demonstrating transitions among stable, periodic, and chaotic processes. These findings offer valuable insights into the complexities of competitive markets and the role of control mechanisms in ensuring stability and efficiency.