Abstract
The aim of the present paper is to analyze the dynamic of a generalized IS‐LM macroeconomic model for the inflation via the use of the averaging theory of dynamical systems. For this 3‐dimensional system we present a rigorous proof on the existence of a limit cycle in the case of considering a nonlinear action of cubic type on the real net product. Moreover we study the stability and the Hopf bifurcations of the system equilibria for different values of the parameters.
► The dynamic of a generalized ISLM macroeconomic model for the inflation using averaging theory is studied. ► A limit cycle is obtained for a non-linear cubic action for real net product. ► Stability and Hopf bifurcations of equilibria are presented. ► The results generalize [V. Torre, Economtrica 45(6), 1457-1466,1977].