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| HAL : hal-00399235, version 1 |
| arXiv : 0906.4842 |
| DOI : 10.1016/j.sysconle.2010.12.004 |
| Fiche détaillée |  Récupérer au format |
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| Systems and Control Letters 60, 3 (2011) 192-197 |
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| Viable harvest of monotone bioeconomic models |
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Michel De Lara 1Pedro Gajardo 2 |
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| STIC--AmSud; ECOS-CONICYT Collaboration(s) |
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| (03/2011) |
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| 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. |
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| 1 : | Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS) |
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Ecole des Ponts ParisTech |
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| 2 : | Universidad Técnica Federico Santa María |
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Universidad Técnica Federico Santa María (UTFSM) |
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| 3 : | Centre de Modélisation Mathématique / Centro de Modelamiento Matemático (CMM) |
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CNRS : UMR2071 |
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| Domaine | : | Mathématiques/Optimisation et contrôle Sciences du Vivant/Ecologie, Environnement |
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| control – viability – monotonicity – reference points – multi-criteria – sustainable management – fisheries |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00399235, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00399235 | |
| oai:hal.archives-ouvertes.fr:hal-00399235 | |
| Contributeur : Michel De Lara | |
| Soumis le : Jeudi 25 Juin 2009, 22:57:02 | |
| Dernière modification le : Jeudi 21 Avril 2011, 10:16:15 | |
