Bifurcation Analysis of a Cournot Triopoly Game with Bounded Rationality and Chaos Control Via the OGY Method

In this study, we explore the dynamics of a triopoly game involving firms with bounded rationality. Our analysis examines the existence and stability of equilibrium points, with a specific focus on the Nash equilibrium point. We found that an increase in the parameters [Formula: see text] (adjustment speed) and [Formula: see text] (product substitution) destabilizes the system, leading to more chaotic behavior through flip and Neimark–Sacker bifurcations. This chaotic behavior is examined through numerical simulations, where various parameters are adjusted to observe their effects. The basins of attraction are analyzed, revealing that the basin of attraction varies as the parameter [Formula: see text] increases. Our approach aims to control the chaotic behavior and stabilize the system by employing the OGY method. Importantly, our analysis emphasizes that the product substitution parameter [Formula: see text] is a key factor in achieving stabilization within the game. To clearly illustrate the effectiveness of our proposed stabilization strategy in this competitive context, we show the numerical simulations.