Hopf Bifurcation and the Existence and Stability of Closed Orbits in Three-Sector Models of Optimal Endogenous Growth

Abstract

The present paper constructs a family of three-sector models of optimal endogenous growth, and conducts ex-act bifurcation analysis. In so doing, original six-dimensional equilibrium dynamics is decomposed into five-dimensional stationary autonomous dynamics and one-dimensional endogenously growing component. It isshown that the stationary dynamics thus decomposed undergoes supercritical Hopf bifurcation. It is inferredfrom the convex structure of our model that the dimension of a stable manifold of each closed orbit thus bifur-cated in this five-dimensional dynamics should be two.