Codimension-One Bifurcation Analysis and Chaos of a Discrete Competition Duopoly Game

This paper examines the temporal evolution of a competitive duopoly game model, emphasizing the identification of significant bifurcation points that influence the system’s dynamics throughout time. The analysis centers on codimension-one bifurcations, specifically two primary categories: flip (period-doubling) bifurcations, potentially leading to quasiperiodic motion on invariant closed curves, and Neimark–Sacker bifurcations, indicative of the onset of periodic or chaotic dynamics. These bifurcations provide substantial insights into the stability, complexity, and strategic interactions between the two competing firms within a nonlinear duopoly framework.