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Papers by Meriem Bentounsi

Research paper thumbnail of Optimization of the Two Fishermen’s Profits Exploiting Three Competing Species Where Prices Depend on Harvest

International Journal of Differential Equations, 2017

Bioeconomic modeling of the exploitation of biological resources such as fisheries has gained imp... more 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 proble...

Research paper thumbnail of A bioeconomic model applied to a small pelagic species along the Moroccan coast

International Journal of Mathematical Modelling and Numerical Optimisation, 2021

Research paper thumbnail of Mathematical study and optimal control of bioeconomic model concerning harmful dinoflagellate phytoplankton

Comput. Appl. Math., 2021

The presence of populations potentially harmful dinoflagellate phytoplankton like Oxyrrhis marina... more The presence of populations potentially harmful dinoflagellate phytoplankton like Oxyrrhis marina requires vigilance and control, because these species, in high density or under certain conditions, can have serious economic consequences and a negative impact on public health. In this investigation, we formulate bioeconomic model of a prey and predator planktonic species. The positivity and boundedness of the solution are studied. The possible equilibriums and their local stability are analyzed; also the global stability of the system around the interior equilibrium is established. We examine the optimal harvesting policy to discuss the dynamical profit of the interacting planktonic species. To show the impact of the toxicity coefficient, we have made analytical estimates that are validated using simulations.

Research paper thumbnail of Catchability coefficient influence on the fishermen's net economic revenues

The present paper describes a prey-predator type fishery model with two predators in competition.... more The present paper describes a prey-predator type fishery model with two predators in competition. The aim of the paper is to maximize the net economic revenue earn from the fishery through implementing the sustainable properties of the fishery to keep the ecological balance. The existence of the steady states and the stability of the interior equilibrium point is studied using Routh Hurwitz criterion. The problem of determining the fishing effort that maximizes the net economic revenue of each fisherman results in a Generalized Nash Equilibrium Problem. More precisely, we are interested in equilibrium of mathematical game given by the situation where all fishermen try to optimize their strategies according to the strategies of all other fishermen. The importance of marine reserve is analyzed through the obtained results of the numerical simulations of proposed model system. The results depict that reserves will be most effective when the coefficient of catchability decreases.

Research paper thumbnail of Mathematical modeling of fishing bioeconomic model including wind speed effects

Research paper thumbnail of Intrinsic growth rates influence on the net economic rents of fishermen

International Journal of Dynamical Systems and Differential Equations, 2019

In this paper, a mathematical model consisting of Sardina pilchardus, Xiphias gladius and Bluefin... more In this paper, a mathematical model consisting of Sardina pilchardus, Xiphias gladius and Bluefin tuna is considered. The differential system is based on the Lotka-Volterra scheme, considering a logistic growth for each population. Biological and bioeconomic equilibria of the system are obtained, and criteria for local stability and instability of the system are derived. This work is an attempt to study the effect of intrinsic growth coefficients changes on the net economic rents of several fishermen exploiting the three marine populations in the Atlantic coast of Morocco based on the parameters given by INRH (Institut National de Recherche Halieutique). To achieve this objective, we have to study the bioeconomic model. Numerical simulations are given to support the theoretical results.

Research paper thumbnail of Mathematical modelling of planktonic organisms

Marine planktonic ecosystems are highly dynamic environments that are subject to a wide range of ... more Marine planktonic ecosystems are highly dynamic environments that are subject to a wide range of external forces [1]. This paper presents the conditions for local and global stability of a bioeconomic problem concerning the harvesting of phytoplankton and zooplankton in Moroccan areas. The problem of determining the fishing effort that maximizes the net economic revenue of each fishing boat results in a Generalized Nash Equilibrium Problem [2,3]. Growth of both organisms is governed by parameters as well as externally applied nutrients and the biomass of the other species available as supplemental nutrition. More precisely, we are interested in the equilibrium of the mathematical game given by the situation where all the fishing boats try to optimize their strategies according to the strategies of all the others [4]. The importance of marine reserve is analyzed through the obtained results of the mathematical analysis of the proposed system.

Research paper thumbnail of 2017-Agmour EtAl-OptimizationofFishermenProfitsExploitingCompetingSpecies

Research paper thumbnail of Bifurcation and stability of a dynamical system with threshold prey harvesting

International Journal of Computing Science and Mathematics

Research paper thumbnail of Carrying capacity influence on the incomes of seiners exploiting marine species in the Atlantic coast of Morocco

Research paper thumbnail of The Impact of Price on the Profits of Fishermen Exploiting Tritrophic Prey-Predator Fish Populations

International Journal of Differential Equations

We define and study a tritrophic bioeconomic model of Lotka-Volterra with a prey, middle predator... more We define and study a tritrophic bioeconomic model of Lotka-Volterra with a prey, middle predator, and top predator populations. These fish populations are exploited by two fishermen. We study the existence and the stability of the equilibrium points by using eigenvalues analysis and Routh-Hurwitz criterion. We determine the equilibrium point that maximizes the profit of each fisherman by solving the Nash equilibrium problem. Finally, following some numerical simulations, we observe that if the price varies, then the profit behavior of each fisherman will be changed; also, we conclude that the price change mechanism improves the fishing effort of the fishermen.

Research paper thumbnail of The Hopf bifurcation and stability of delayed predator–prey system

Computational and Applied Mathematics

Research paper thumbnail of Stability Analysis of a Biological Model of a Marine Resources Allowing Density Dependent Migration

International Frontier Science Letters

Biology of a marine resources is a descriptive science. The description is the first step towards... more Biology of a marine resources is a descriptive science. The description is the first step towards understanding a system. However, the main objective is to present a rigorous mathematical analysis and numerical simulation of these spatio temporal models. In the present paper, we consider a two species food chain, i.e. a prey and predator populations modeled in a two-patch environment, one of which is a free fishing zone and the other one is protected zone. We study the qualitative analysis of solutions and we establish sufficient conditions under which the endemic and trivial equilibria are asymptotically stable.The asymptotic stability corresponding to the equilibria is graphically shown.

Research paper thumbnail of Optimization of the Two Fishermen’s Profits Exploiting Three Competing Species Where Prices Depend on Harvest

International Journal of Differential Equations, 2017

Bioeconomic modeling of the exploitation of biological resources such as fisheries has gained imp... more 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 proble...

Research paper thumbnail of A bioeconomic model applied to a small pelagic species along the Moroccan coast

International Journal of Mathematical Modelling and Numerical Optimisation, 2021

Research paper thumbnail of Mathematical study and optimal control of bioeconomic model concerning harmful dinoflagellate phytoplankton

Comput. Appl. Math., 2021

The presence of populations potentially harmful dinoflagellate phytoplankton like Oxyrrhis marina... more The presence of populations potentially harmful dinoflagellate phytoplankton like Oxyrrhis marina requires vigilance and control, because these species, in high density or under certain conditions, can have serious economic consequences and a negative impact on public health. In this investigation, we formulate bioeconomic model of a prey and predator planktonic species. The positivity and boundedness of the solution are studied. The possible equilibriums and their local stability are analyzed; also the global stability of the system around the interior equilibrium is established. We examine the optimal harvesting policy to discuss the dynamical profit of the interacting planktonic species. To show the impact of the toxicity coefficient, we have made analytical estimates that are validated using simulations.

Research paper thumbnail of Catchability coefficient influence on the fishermen's net economic revenues

The present paper describes a prey-predator type fishery model with two predators in competition.... more The present paper describes a prey-predator type fishery model with two predators in competition. The aim of the paper is to maximize the net economic revenue earn from the fishery through implementing the sustainable properties of the fishery to keep the ecological balance. The existence of the steady states and the stability of the interior equilibrium point is studied using Routh Hurwitz criterion. The problem of determining the fishing effort that maximizes the net economic revenue of each fisherman results in a Generalized Nash Equilibrium Problem. More precisely, we are interested in equilibrium of mathematical game given by the situation where all fishermen try to optimize their strategies according to the strategies of all other fishermen. The importance of marine reserve is analyzed through the obtained results of the numerical simulations of proposed model system. The results depict that reserves will be most effective when the coefficient of catchability decreases.

Research paper thumbnail of Mathematical modeling of fishing bioeconomic model including wind speed effects

Research paper thumbnail of Intrinsic growth rates influence on the net economic rents of fishermen

International Journal of Dynamical Systems and Differential Equations, 2019

In this paper, a mathematical model consisting of Sardina pilchardus, Xiphias gladius and Bluefin... more In this paper, a mathematical model consisting of Sardina pilchardus, Xiphias gladius and Bluefin tuna is considered. The differential system is based on the Lotka-Volterra scheme, considering a logistic growth for each population. Biological and bioeconomic equilibria of the system are obtained, and criteria for local stability and instability of the system are derived. This work is an attempt to study the effect of intrinsic growth coefficients changes on the net economic rents of several fishermen exploiting the three marine populations in the Atlantic coast of Morocco based on the parameters given by INRH (Institut National de Recherche Halieutique). To achieve this objective, we have to study the bioeconomic model. Numerical simulations are given to support the theoretical results.

Research paper thumbnail of Mathematical modelling of planktonic organisms

Marine planktonic ecosystems are highly dynamic environments that are subject to a wide range of ... more Marine planktonic ecosystems are highly dynamic environments that are subject to a wide range of external forces [1]. This paper presents the conditions for local and global stability of a bioeconomic problem concerning the harvesting of phytoplankton and zooplankton in Moroccan areas. The problem of determining the fishing effort that maximizes the net economic revenue of each fishing boat results in a Generalized Nash Equilibrium Problem [2,3]. Growth of both organisms is governed by parameters as well as externally applied nutrients and the biomass of the other species available as supplemental nutrition. More precisely, we are interested in the equilibrium of the mathematical game given by the situation where all the fishing boats try to optimize their strategies according to the strategies of all the others [4]. The importance of marine reserve is analyzed through the obtained results of the mathematical analysis of the proposed system.

Research paper thumbnail of 2017-Agmour EtAl-OptimizationofFishermenProfitsExploitingCompetingSpecies

Research paper thumbnail of Bifurcation and stability of a dynamical system with threshold prey harvesting

International Journal of Computing Science and Mathematics

Research paper thumbnail of Carrying capacity influence on the incomes of seiners exploiting marine species in the Atlantic coast of Morocco

Research paper thumbnail of The Impact of Price on the Profits of Fishermen Exploiting Tritrophic Prey-Predator Fish Populations

International Journal of Differential Equations

We define and study a tritrophic bioeconomic model of Lotka-Volterra with a prey, middle predator... more We define and study a tritrophic bioeconomic model of Lotka-Volterra with a prey, middle predator, and top predator populations. These fish populations are exploited by two fishermen. We study the existence and the stability of the equilibrium points by using eigenvalues analysis and Routh-Hurwitz criterion. We determine the equilibrium point that maximizes the profit of each fisherman by solving the Nash equilibrium problem. Finally, following some numerical simulations, we observe that if the price varies, then the profit behavior of each fisherman will be changed; also, we conclude that the price change mechanism improves the fishing effort of the fishermen.

Research paper thumbnail of The Hopf bifurcation and stability of delayed predator–prey system

Computational and Applied Mathematics

Research paper thumbnail of Stability Analysis of a Biological Model of a Marine Resources Allowing Density Dependent Migration

International Frontier Science Letters

Biology of a marine resources is a descriptive science. The description is the first step towards... more Biology of a marine resources is a descriptive science. The description is the first step towards understanding a system. However, the main objective is to present a rigorous mathematical analysis and numerical simulation of these spatio temporal models. In the present paper, we consider a two species food chain, i.e. a prey and predator populations modeled in a two-patch environment, one of which is a free fishing zone and the other one is protected zone. We study the qualitative analysis of solutions and we establish sufficient conditions under which the endemic and trivial equilibria are asymptotically stable.The asymptotic stability corresponding to the equilibria is graphically shown.