scholarly journals The Impact of Price on the Profits of Fishermen Exploiting Tritrophic Prey-Predator Fish Populations

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Meriem Bentounsi ◽  
Imane Agmour ◽  
Naceur Achtaich ◽  
Youssef El Foutayeni
Keyword(s):  
Equilibrium Points ◽  
Price Change ◽  
Fishing Effort ◽  
Fish Populations ◽  
Bioeconomic Model ◽  
Top Predator ◽  
Nash Equilibrium Problem ◽  
Change Mechanism ◽  
The Stability ◽  
The Impact

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.

scholarly journals The Tide Effects on Bioeconomic Model of Sardina pilchardus, Engraulis encrasicolus and Xiphias gladius in Atlantic Moroccan Zone

2021 ◽  
Author(s):  
Nossaiba Baba ◽  
Imane Agmour ◽  
Youssef El Foutayeni ◽  
Naceur Achtaich
Keyword(s):  
Equilibrium Points ◽  
Marine Species ◽  
Fishing Effort ◽  
Generalized Nash Equilibrium ◽  
Bioeconomic Model ◽  
Sardina Pilchardus ◽  
Engraulis Encrasicolus ◽  
Xiphias Gladius ◽  
The Stability ◽  
Bioeconomic Models

AbstractThe main objective of this work is the study of the effects of high tides and low tides on fishing effort, catches as well as profits in a bioeconomic model of populations of Sardina pilchardus, Engraulis encrasicolus and Xiphias gladius in Moroccan areas. To achieve this objective, we studied the stability of the equilibrium points of our biological model then we added in our model the effect of the tides in the fishing effort which maximizes the profits of the fishermen under the constraint of the conservation of the biodiversity of these marine species using the generalized Nash equilibrium in the resolution of the bioeconomic model. As results, we were able to give the best fishing times according to the tides of each month of the whole year which will allow us to achieve better yields. Hence the importance of introducing the effect of high and low tides in bioeconomic models.

On the stability of a mathematical model for HIV(AIDS) - cancer dynamics

2021 ◽  
Vol 8 (4) ◽  
pp. 783-796
Author(s):  
H. W. Salih ◽  
◽  
A. Nachaoui ◽  
Keyword(s):  
Mathematical Model ◽  
Highly Active Antiretroviral Therapy ◽  
Lyapunov Method ◽  
Equilibrium Points ◽  
Hiv Treatment ◽  
Biochemical Processes ◽  
Highly Active ◽  
Biological Phenomena ◽  
The Stability ◽  
The Impact

In this work, we study an impulsive mathematical model proposed by Chavez et al. [1] to describe the dynamics of cancer growth and HIV infection, when chemotherapy and HIV treatment are combined. To better understand these complex biological phenomena, we study the stability of equilibrium points. To do this, we construct an appropriate Lyapunov function for the first equilibrium point while the indirect Lyapunov method is used for the second one. None of the equilibrium points obtained allow us to study the stability of the chemotherapeutic dynamics, we then propose a bifurcation of the model and make a study of the bifurcated system which contributes to a better understanding of the underlying biochemical processes which govern this highly active antiretroviral therapy. This shows that this mathematical model is sufficiently realistic to formulate the impact of this treatment.

scholarly journals Bifurcation analysis and optimal control of SEIR epidemic model with saturated treatment function on the network

2021 ◽  
Vol 19 (2) ◽  
pp. 1677-1695
Author(s):  
Boli Xie ◽  
◽  
Maoxing Liu ◽  
Lei Zhang
Keyword(s):  
Optimal Control ◽  
Disease Transmission ◽  
Equilibrium Points ◽  
Virus Transmission ◽  
Population Heterogeneity ◽  
Multiple Equilibrium ◽  
Optimal Control Strategy ◽  
Treatment Function ◽  
The Stability ◽  
The Impact

<abstract><p>In order to study the impact of limited medical resources and population heterogeneity on disease transmission, a SEIR model based on a complex network with saturation processing function is proposed. This paper first proved that a backward bifurcation occurs under certain conditions, which means that $ R_{0} &lt; 1 $ is not enough to eradicate this disease from the population. However, if the direction is positive, we find that within a certain parameter range, there may be multiple equilibrium points near $ R_{0} = 1 $. Secondly, the influence of population heterogeneity on virus transmission is analyzed, and the optimal control theory is used to further study the time-varying control of the disease. Finally, numerical simulations verify the stability of the system and the effectiveness of the optimal control strategy.</p></abstract>

Fear Induced Stabilization in an Intraguild Predation Model

2020 ◽  
Vol 30 (04) ◽  
pp. 2050053
Author(s):  
Mainul Hossain ◽  
Nikhil Pal ◽  
Sudip Samanta ◽  
Joydev Chattopadhyay
Keyword(s):  
Growth Rate ◽  
Hopf Bifurcation ◽  
Intraguild Predation ◽  
Equilibrium Points ◽  
Stable Limit ◽  
Interior Equilibrium ◽  
The Rich ◽  
The Stability ◽  
The Cost ◽  
The Impact

In the present paper, we investigate the impact of fear in an intraguild predation model. We consider that the growth rate of intraguild prey (IG prey) is reduced due to the cost of fear of intraguild predator (IG predator), and the growth rate of basal prey is suppressed due to the cost of fear of both the IG prey and the IG predator. The basic mathematical results such as positively invariant space, boundedness of the solutions, persistence of the system have been investigated. We further analyze the existence and local stability of the biologically feasible equilibrium points, and also study the Hopf-bifurcation analysis of the system with respect to the fear parameter. The direction of Hopf-bifurcation and the stability properties of the periodic solutions have also been investigated. We observe that in the absence of fear, omnivory produces chaos in a three-species food chain system. However, fear can stabilize the chaos thus obtained. We also observe that the system shows bistability behavior between IG prey free equilibrium and IG predator free equilibrium, and bistability between IG prey free equilibrium and interior equilibrium. Furthermore, we observe that for a suitable set of parameter values, the system may exhibit multiple stable limit cycles. We perform extensive numerical simulations to explore the rich dynamics of a simple intraguild predation model with fear effect.

A COMPARTMENTAL MODEL OF SLEEPING SICKNESS IN CENTRAL AFRICA

1996 ◽  
Vol 04 (04) ◽  
pp. 459-477 ◽  
Author(s):  
MARC ARTZROUNI ◽  
JEAN-PAUL GOUTEUX
Keyword(s):  
Compartmental Model ◽  
Equilibrium Points ◽  
Central Africa ◽  
Sleeping Sickness ◽  
Tsetse Flies ◽  
Reproduction Rate ◽  
Basic Reproduction Rate ◽  
The Stability ◽  
The Impact ◽  
Percent Decrease

We present a five-variable compartmental model for the spread of Trypanosoma brucei gambiense, the parasite responsible for the transmission (through tsetse flies) of sleeping sickness in Central Africa. The model’s equilibrium points depend on two “summary parameters”: gr, the proportion removed among human infectives, and R0, the basic reproduction rate. Stability results are obtained for the origin but not for other equilibrium points. A two-variable simplified version of the model is presented and the stability of all its equilibrium points can be investigated analytically. Both models are applied to the Niari focus of Central Africa and used to test the impact of a vector control strategy. The models’ results are in agreement with the extinction of the epidemic that was brought about by a fifty percent decrease in vector density.

scholarly journals Quantifying relative fishing impact on fish populations based on spatio-temporal overlap of fishing effort and stock density

2013 ◽  
Vol 70 (3) ◽  
pp. 618-627 ◽  
Author(s):  
Morten Vinther ◽  
Margit Eero
Keyword(s):  
Fishing Effort ◽  
Fish Populations ◽  
Fishing Mortality ◽  
Fishing Impact ◽  
Management Measures ◽  
Stock Assessments ◽  
Spatio Temporal ◽  
Substantial Decline ◽  
The Impact ◽  
Temporal Overlap

Abstract Vinther, M., and Eero, M. 2013. Quantifying relative fishing impact on fish populations based on spatio-temporal overlap of fishing effort and stock density. – ICES Journal of Marine Science, 70: 618–627. Evaluations of the effects of management measures on fish populations are usually based on the analyses of population dynamics and estimates of fishing mortality from stock assessments. However, this approach may not be applicable in all cases, in particular for data-limited stocks, which may suffer from uncertain catch information and consequently lack reliable estimates of fishing mortality. In this study we develop an approach to obtain proxies for changes in fishing mortality based on effort information and predicted stock distribution. Cod in the Kattegat is used as an example. We use GAM analyses to predict local cod densities and combine this with spatio-temporal data of fishing effort based on VMS (Vessel Monitoring System). To quantify local fishing impact on the stock, retention probability of the gears is taken into account. The results indicate a substantial decline in the impact of the Danish demersal trawl fleet on cod in the Kattegat in recent years, due to a combination of closed areas, introduction of selective gears and changes in overall effort.

scholarly journals A fractional-order love dynamical model with time delay for synergic couple : Stability analysis and Hopf bifurcation

2021 ◽  
Author(s):  
SANTOSHI PANIGRAHI ◽  
Sunita Chand ◽  
S Balamuralitharan
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Fractional Order ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Order Model ◽  
Fractional Order Model ◽  
The Stability ◽  
The Impact

We investigate the fractional order love dynamic model with time delay for synergic couples in this manuscript. The quantitative analysis of the model has been done where the asymptotic stability of the equilibrium points of the model have been analyzed. Under the impact of time delay, the Hopf bifurcation analysis of the model has been done. The stability analysis of the model has been studied with the reproduction number less than or greater than 1. By using Laplace transformation, the analysis of the model has been done. The analysis shows that the fractional order model with a time delay can sufficiently improve the components and invigorate the outcomes for either stable or unstable criteria. In this model, all unstable cases are converted to stable cases under neighbourhood points. For all parameters, the reproduction ranges have been described. Finally, to illustrate our derived results numerical simulations have been carried out by using MATLAB. Under the theoretical outcomes from parameter estimation, the love dynamical system is verified.

scholarly journals Transmission Dynamics of Resistant Bacteria in a Predator-Prey System

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Xubin Gao ◽  
Qiuhui Pan ◽  
Mingfeng He
Keyword(s):  
Human Health ◽  
Large Scale ◽  
Equilibrium Points ◽  
Predation Rate ◽  
Resistant Bacteria ◽  
Mathematical Methods ◽  
Predator Prey ◽  
Prey System ◽  
The Stability ◽  
The Impact

This paper discusses the impact on human health caused by the addition of antibiotics in the feed of food animals. We use the established transmission rule of resistant bacteria and combine it with a predator-prey system to determine a differential equations model. The equations have three steady equilibrium points corresponding to three population dynamics states under the influence of resistant bacteria. In order to quantitatively analyze the stability of the equilibrium points, we focused on the basic reproduction numbers. Then, both the local and global stability of the equilibrium points were quantitatively analyzed by using essential mathematical methods. Numerical results are provided to relate our model properties to some interesting biological cases. Finally, we discuss the effect of the two main parameters of the model, the proportion of antibiotics added to feed and the predation rate, and estimate the human health impacts related to the amount of feed antibiotics used. We further propose an approach for the prevention of the large-scale spread of resistant bacteria and illustrate the necessity of controlling the amount of in-feed antibiotics used.

The chaotic dynamics of a quantum Cournot duopoly game with bounded rationality

2020 ◽  
Vol 18 (06) ◽  
pp. 2050029
Author(s):  
Xinli Zhang ◽  
Deshan Sun ◽  
Wei Jiang
Keyword(s):  
Quantum Entanglement ◽  
Stability Region ◽  
Chaotic Dynamics ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Largest Lyapunov Exponent ◽  
Cournot Duopoly ◽  
The Stability ◽  
The Impact ◽  
Rational Players

This paper analyzes the chaotic dynamics of a quantum Cournot duopoly game with bounded rational players by applying quantum game theory. We investigate the impact of quantum entanglement on the stability of the quantum Nash equilibrium points and chaotic dynamics behaviors of the system. The result shows that the stability region decreases with the quantum entanglement increasing. The adjustment speeds of bounded rational players can lead to chaotic behaviors, and quantum entanglement accelerates the bifurcation and chaos of the system. Numerical simulations demonstrate the chaotic features via stability region, bifurcation, largest Lyapunov exponent, strange attractors, sensitivity to initial conditions and fractal dimensions.

scholarly journals Analysis of the Financial Chaotic Model with the Fractional Derivative Operator

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Mamadou Diouf ◽  
Ndolane Sene
Keyword(s):  
Equilibrium Points ◽  
Direct Methods ◽  
Saving Rate ◽  
Financial Model ◽  
Chaotic Model ◽  
Investment Cost ◽  
Fractional Differential ◽  
Numerical Discretization ◽  
The Stability ◽  
The Impact

Numerical discretization for the fractional differential equations is applied to the chaotic financial model described by the Caputo derivative. The graphical representations to support the numerical discretization are presented. We profit by analyzing the impact generated by the variations of the saving rate, the per investment cost, and the elasticity of demands in the dynamics of the solutions obtained with our numerical scheme. Notably, we use bifurcation diagrams to quantify the impact of the saving rate, the per investment cost, and the elasticity of demands, as well as the Lyapunov exponent to characterize the existence of chaos for the chosen value of the fractional order. The chaos observed depends strongly on these previously mentioned parameters. We finish by proposing a suitable control to synchronize the drive system and the response fractional financial model, using Lyapunov direct methods. The stability analysis of the equilibrium points of the chaotic financial model has been presented.

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