Bifurcation analysis and chaos control of a discret duopoly model.

Abstract

In this work, we have outlined some tools to study dynamical systems, such as equilibrium points, stability, bifurcations, and chaos, as well as some control methods, the chaotic attractor, and Lyapunov exponents. As an application, we studied a duopoly model consisting of two different equations, where each equation represents a player, and each player seeks to maximize their profits and market share using different strategies. The results obtained in this work contribute to a better understanding of complex financial markets and to the improvement of the development of more accurate and efficient economic models. It is useful for financial analysts and investors to improve their strategies and reduce risks. The results indicate several important aspects: the stability of equilibrium points, bifurcations, and chaos, where the results indicate the existence of bifurcations at equilibrium solutions (Flip, Neimark Sacker), as well as the presence of a chaotic attractor that was controlled by the OGY method. In addition, numerical simulation was used to confirm the results obtained theoretically.