Ly S., Auger Pierre, Balde M. (2014). A bioeconomic model of a multi-site fishery with nonlinear demand function : number of sites optimizing the total catch. Acta Biotheoretica, 62 (3), p. 371-384. ISSN 0001-5342.
Titre du document
A bioeconomic model of a multi-site fishery with nonlinear demand function : number of sites optimizing the total catch
Acta Biotheoretica, 2014,
62 (3), p. 371-384 ISSN 0001-5342
We present a mathematical model of a fishery on several sites with a variable price. The model takes into account the evolution during the time of the resource, fish and boat movement between the different sites, fishing effort and price that varies with respect to supply and demand. We suppose that the movements of the boats and resource as well as the variation of the price go on at a fast time scale. We use methods of aggregation of variables in order to reduce the number of variables and we derive a reduced model governing two global variables, respectively the biomass of the resource and the fishing effort of the whole fishery. We look for the existence of equilibria of the aggregated model and perform local stability analysis. Two main cases can occur. The first one corresponds to over-exploitation leading to fish extinction. At extinction, the fishing effort tends to a positive value. The second case corresponds to a durable fishery equilibrium which is globally asymptotically stable. In the later case, we show that there exists a number of fishing sites that optimizes the total catch of the fishery.
Plan de classement
Sciences fondamentales / Techniques d'analyse et de recherche [020]
;
Ressources halieutiques [040]
