Global Indeterminacy and Invariant Manifolds near Homoclinic Orbit to a Real Saddle in a Resource Optimal System

The paper investigates the dynamic properties of a resource optimal system with externality derived by [1]. To this end, we determine the whole set of conditions that lead to global indeterminacy and the existence of a homoclinic orbit that converges in both forward and backward time to a real saddle equilibrium 5 points. The dynamics near this homoclinic orbit have been investigated. If the exponent of the externality is varied the homoclinic is broken and it bifurcates in a stable periodic orbit. The economic implications are discussed in the conclusions