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Optimization of the Two Fishermen’s Profits Exploiting Three Competing Species Where Prices Depend on Harvest
Joint Authors
Agmour, Imane
Bentounsi, Meriem
Achtaich, Naceur
El Foutayeni, Youssef
Source
International Journal of Differential Equations
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-17, 17 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-12-26
Country of Publication
Egypt
No. of Pages
17
Main Subjects
Abstract EN
Bioeconomic modeling of the exploitation of biological resources such as fisheries has gained importance in recent years.
In this work we propose to define and study a bioeconomic equilibrium model for two fishermen who catch three species taking into consideration the fact that the prices of fish populations vary according to the quantity harvested; these species compete with each other for space or food; the natural growth of each species is modeled using a logistic law.
The main purpose of this work is to define the fishing effort that maximizes the profit of each fisherman, but all of them have to respect two constraints: the first one is the sustainable management of the resources and the second one is the preservation of the biodiversity.
The existence of the steady states and their stability are studied using eigenvalue analysis.
The problem of determining the equilibrium point that maximizes the profit of each fisherman leads to Nash equilibrium problem; to solve this problem we transform it into a linear complementarity problem (LCP); then we prove that the obtained problem (LCP) admits a unique solution that represents the Nash equilibrium point of our problem.
We close our paper with some numerical simulations.
American Psychological Association (APA)
Agmour, Imane& Bentounsi, Meriem& Achtaich, Naceur& El Foutayeni, Youssef. 2017. Optimization of the Two Fishermen’s Profits Exploiting Three Competing Species Where Prices Depend on Harvest. International Journal of Differential Equations،Vol. 2017, no. 2017, pp.1-17.
https://search.emarefa.net/detail/BIM-1165833
Modern Language Association (MLA)
Agmour, Imane…[et al.]. Optimization of the Two Fishermen’s Profits Exploiting Three Competing Species Where Prices Depend on Harvest. International Journal of Differential Equations No. 2017 (2017), pp.1-17.
https://search.emarefa.net/detail/BIM-1165833
American Medical Association (AMA)
Agmour, Imane& Bentounsi, Meriem& Achtaich, Naceur& El Foutayeni, Youssef. Optimization of the Two Fishermen’s Profits Exploiting Three Competing Species Where Prices Depend on Harvest. International Journal of Differential Equations. 2017. Vol. 2017, no. 2017, pp.1-17.
https://search.emarefa.net/detail/BIM-1165833
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1165833