Math. Model. Nat. Phenom.
Volume 8, Number 6, 2013Ecology
|Page(s)||130 - 142|
|Published online||28 November 2013|
A Model of a Multi-Site Fishery with Variable Price: from Over-Exploitation to Sustainable Fisheries
1 Université Cheikh-Anta-Diop, Dakar, Sénégal
2 IRD UMI IMMISCO, 32 av. Henri Varagnat, 93140 Bondy cedex, France
3 IXXI, ENS Lyon, 15 parvis René Descartes, BP 7000, 69342 Lyon Cedex 07
Corresponding author. E-mail: firstname.lastname@example.org
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, fishes and boats movements between the different sites, fishing effort and price that varies with respect to supply and demand. We suppose that boats and fishes movements as well as prices variations occur 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. We show that the aggregated model can have 1, 2 or 3 non trivial equilibria. We show that a variation of the total number of sites can induce a switch from over-exploitation to sustainable fisheries.
Mathematics Subject Classification: 92D25 / 91B276 / 34A33
Key words: dynamical systems / multi-site fishery / variable price / demand function / equilibrium / stability / optimum capture
© EDP Sciences, 2013
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