On the dynamics of an inflation IS‐LM model

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.