Viable harvest of monotone bioeconomic models

Michel de Lara (1) , Pedro Gajardo (2) , Hector Ramirez Cabrera (3)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 Departamento de Matematica [Valparaiso]
3 CMM - Centre de modélisation mathématique / Centro de Modelamiento Matemático [Santiago]

Some monospecies age class models, as well as specific multi-species models (with so-called technical interactions), exhibit useful monotonicity properties. This paper deals with discrete time monotone bioeconomics dynamics in the presence of state and control constraints. In practice, these latter ``acceptable configurations'' represent production and preservation requirements to be satisfied for all time, and they also possess monotonicity properties. A state $\state$ is said to belong to the viability kernel if there exists a trajectory, of states and controls, starting from $\state$ and satisfying the constraints. Under monotonicity assumptions, we present upper and lower estimates of the viability kernel. This helps delineating domains where a viable management is possible. Numerical examples, in the context of fisheries management, for the Chilean sea bass (\emph{Dissostichus eleginoides}) and Alfonsino (\emph{Beryx splendens}) are given.

Mots clés: control; viability; monotonicity; reference points; multi-criteria; sustainable management; fisheries

Domaines: Optimisation et contrôle [math.OC]; Ecologie, Environnement

Michel de Lara, Pedro Gajardo, Hector Ramirez Cabrera. Viable harvest of monotone bioeconomic models. Systems and Control Letters, 2011, 60 (3), pp.192-197. ⟨10.1016/j.sysconle.2010.12.004⟩. ⟨hal-00399235⟩