Viability analysis for the sustainable management of renewable resources

We consider an age-structured discrete time modeling of a renewable resource, controlled by the harvesting of the mature class. A harvesting policy is considered to be sustainable if a minimum harvesting threshold can be guaranteed at any time, taking into account availability constraints. For the characterization of such policies, viability analysis reveals the intrinsic compatibility of the dynamics within a given threshold. Formulae for the maximal sustainable threshold that can be maintained by the resource, viability kernels and the set of corresponding sustainable feedbacks are obtained. We then propose explicit management rules, maximizing the sustainable threshold, and illustrate them with numerical simulations for two kinds of resources.