Bifurcations and sunspots in continuous time optimal models with externalities

In this chapter, we construct sunspot equilibria in a class of continuous-time optimal control models with externalities. The model possesses stochastic characteristics which arise from indeterminate equilibrium and cycles (Hopf cycles) closed to the steady state. The model undergoes to Hopf bifurcations in some parameters set. We construct a stationary sunspot equilibrium near the closed orbit. We show that the stochastic approach suggests a way out from the poverty environments trap in a natural resource optimal model.