Viability Kernel for Ecosystem Management Models

Eladio Ocana Anaya (1) , Michel de Lara (2) , Ricardo Oliveros--Ramos (3, 4) , Jorge Tam (3, 4)

1 IMCA - Instituto de Matematica y Ciencias Afines
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
3 IMARPE - Instituto del Mar del Peru
4 Research Center for Oceanographic and Biological Fishery Modelling (CIMOBP)

We consider sustainable management issues formulated within the framework of control theory. The problem is one of controlling a discrete--time dynamical system (e.g. population model) in the presence of state and control constraints, representing conflicting economic and ecological issues for instance. The viability kernel is known to play a basic role for the analysis of such problems and the design of viable control feedbacks, but its computation is not an easy task in general. We study the viability of nonlinear generic ecosystem models under preservation and production constraints. Under simple conditions on the growth rates at the boundary constraints, we provide an explicit description of the viability kernel. A numerical illustration is given for the hake--anchovy couple in the Peruvian upwelling ecosystem.

Mots clés: control theory; state constraints; viability; predator--prey; ecosystem management; Peruvian upwelling ecosystem

Domaines: Optimisation et contrôle [math.OC]

Eladio Ocana Anaya, Michel de Lara, Ricardo Oliveros--Ramos, Jorge Tam. Viability Kernel for Ecosystem Management Models. 2009. ⟨hal-00390822⟩