22066 articles – 15901 references  [version française]
 HAL: hal-00399235, version 1
 arXiv: 0906.4842
 Systems and Control Letters 60, 3 (2011) 192-197
 Viable harvest of monotone bioeconomic models
 Michel De Lara ( ) 1, Pedro Gajardo 2
 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 ControlLife Sciences/Ecology, environment
 Keyword(s): control – viability – monotonicity – reference points – multi-criteria – sustainable management – fisheries
Attached file list to this document:
 PDF
 JMB_monotone_20090625.pdf(251 KB)
 PS
 JMB_monotone_20090625.ps(312 KB)
 hal-00399235, version 1 http://hal.archives-ouvertes.fr/hal-00399235 oai:hal.archives-ouvertes.fr:hal-00399235 From: Michel De Lara <> Submitted on: Thursday, 25 June 2009 22:57:02 Updated on: Thursday, 21 April 2011 10:16:15