Qualitative behavior in a fractional order IS-LM-AS macroeconomic model with stability analysis

Abstract

In this article, we analyze the conditions for the structural stability of a fractional order IS-LM-AS dynamic model with adaptive expectations. It is a generalization of our previous research lately published in the literature. We also present the conditions that the structural parameters of the model must meet for the economic system to present a periodic movement when the critical value of the fractional order of the system, q* , guarantees the presence of a Hopf bifurcation of degenerate type. The theoretical analysis is complemented with numerical simulations of the phase portraits in R3 and of the temporal trajectories of the solutions of the model in MATLAB software. Finally, it is important to highlight that unlike the results of our previous research, the qualitative results found in this paper show that all the structural parameters of the model are essential in determining its global asymptotic stability and Hopf bifurcation.