Bifurcations and chaos in a novel discrete economic system

Abstract

In this article, a novel discrete system based on an economic model is introduced. Conditions for local stability of the model’s fixed points are obtained. Existence of supercritical Neimark–Sacker bifurcation is shown around the game’s Nash equilibrium. Existence of stable period-2 orbits resulting from flip bifurcation around the game’s Nash equilibrium is also proved. Existence of chaotic dynamics in the proposed game is also shown via two routes: Neimark–Sacker bifurcation and flip bifurcation. Based on the bifurcation theory of discrete-time systems, sufficient conditions of transcritical bifurcation are derived and applied to the proposed model. The interesting phenomenon of coexisting multi-chaotic attractors, such as coexistence of two, three, four, and five-piece chaotic attractors, is found in the proposed model. For this reason, numerical simulations of basins of attraction are performed to verify the appearance of this important phenomenon that reflects the unpredictability and higher complexity in the proposed game.