Existence and Stability of Periodic Solutions in the Dynamics of Endogenous Growth

As clearly testified by the most recent literature, a rich array of outcomes, other than saddle-path trajectories, can easily emerge in endogenous growth models, particularly when an externality parameter is introduced. By applying bifurcation theory to a reduced form of Lucas’s celebrated model on the mechanics of endogenous growth (1988) we produce evidence of the existence of closed orbits Hopf bifurcating from a saddle-focus for special regions of the parameter space. The stability of these cycles on the center manifold is also investigated.