HAL: hal-00399235, version 1

arXiv: 0906.4842

DOI: 10.1016/j.sysconle.2010.12.004

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Systems and Control Letters 60, 3 (2011) 192-197

Viable harvest of monotone bioeconomic models

Michel De Lara (  Corresponding author ) 1, Pedro Gajardo 2, Hector Ramirez Cabrera 3

For the STIC--AmSud; ECOS-CONICYT collaboration(s)

(2011-03)

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.

1:	Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS)
	Ecole des Ponts ParisTech
2:	Universidad Técnica Federico Santa María
	Universidad Técnica Federico Santa María (UTFSM)
3:	Centre de Modélisation Mathématique / Centro de Modelamiento Matemático (CMM)
	CNRS : UMR2071

Subject

:

Mathematics/Optimization and Control Life Sciences/Ecology, environment

Keyword(s): control – viability – monotonicity – reference points – multi-criteria – sustainable management – fisheries

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From: Michel De Lara <>

Submitted on: Thursday, 25 June 2009 22:57:02

Updated on: Thursday, 21 April 2011 10:16:15