Generic and symmetric bifurcations analysis of a three dimensional economic model

Abstract

Abstract This paper studies bifurcation analysis of an economic model by using the critical normal form coefficients method which is one of the most influential methods in bifurcation theory. This method advantageously checks the non-degeneracy condition without computing the central manifold and converting the linear part of the map into Jordan form. In this study, the codimension one and codimension two bifurcations of the model are investigated by considering different parameters and for each bifurcation, the normal form coefficients are computed. The obtained results conclude that the model undergoes bifurcations such as flip (period-doubling), Neimark-Sacker, resonance 1:3, resonance 1:4, Chenciner and period-doubling Neimark-Sacker. Furthermore, to accomplish symmetric bifurcation analysis of the model, the normal form of the Z 3 -symmetric double-1 multiplier bifurcation is utilized. The bifurcation curves of the model are drawn with the aid of the numerical continuation method. From the mathematical point of view, these bifurcation curves and numerical simulations not only support the theoretical results but also reveal more details of the dynamic system under study, especially after higher iterations. The achieved results directly can be applied to design and optimize many types of economic models.