Hybrid dynamics of multi-species resource exploitation

Abstract

In this paper, we analyze a bio-economic model of exploitation of renewable commercial resources. To take into account the typically continuous-time modeling of biological species and, instead, of the specialized harvesting activities, which by its nature cannot change continuously, the resulting dynamic system is of the hybrid type, i.e. continuous for biological variables and discrete for the economic ones. Through a discretization of the continuous variables, the problem is then reformulated by means of a three-dimensional map. Of this map, we study the dynamic properties to understand how economic parameters influence the long-run availability of resources.