Asymptotic Convergence of Optimal Policies for Resource Management with Application to Harvesting of Multiple Species Forest

We study the long-term behavior of the optimal harvesting policies for a mixed forest composed by multiple species of different maturity ages. This model is a prototype for the exploitation of a finite resource such as land or space, which can be allocated to different activities that produce their revenue after certain delays at which the resource is liberated for reuse. We prove the existence and uniqueness of a sustainable state, and we discuss the conditions under which an optimal trajectory converges in the long run toward this state or toward the set of optimal periodic cycles. We also analyze different situations in which the convergence occurs in finite time.