A SUFFICIENT CONDITION OF A POLYNOMIAL FISH POPULATION SYSTEM TO BE STABLE

2012 ◽  
Vol 03 (03) ◽  
pp. 1250012
Author(s):  
YOUNES LOUARTASSI ◽  
EL HOUSSINE EL MAZOUDI ◽  
NOUREDDINE ELALAMI
Keyword(s):  
Polynomial System ◽  
Sufficient Conditions ◽  
Fish Population ◽  
Age Classes ◽  
Population System ◽  
Control Engineering ◽  
Lyapunov Approach ◽  
Computational Implementation ◽  
Stock Recruitment ◽  
The Stability

In this paper, we use Lyapunov approach to study the stability of an exploited fish population system. The model considered is structured in n age classes and includes a nonlinear polynomial stock-recruitment relationship. Lyapunov candidate functions is investigated and sufficient conditions for global asymptotic stability of the studied polynomial system are proposed to allow computational implementation. The results obtained extend our previous study focusing on the solution to the same problem solved using other tools of control engineering. The advantage of the proposed approach is that the derived conditions proving the stability of the studied systems can be presented as in inequality in general and feasibility tests. The obtained results are tested by numerical examples.

Responses of a Fish Population Model to Young-of-the-Year Mortality

1977 ◽  
Vol 34 (11) ◽  
pp. 2117-2123 ◽  
Author(s):  
D. L. DeAngelis ◽  
S. W. Christensen ◽  
A. G. Clark
Keyword(s):  
Larval Fish ◽  
Population Decline ◽  
Fish Population ◽  
Leslie Matrix ◽  
Class Model ◽  
Stock Recruitment ◽  
Young Of The Year ◽  
Mortality Causes ◽  
The Stability ◽  
Population Numbers

A multiple-age-class model is used to examine the effects of increases in density-independent young-of-the-year mortality caused by power plant entrainment of larval fish. It is demonstrated analytically that in all realistic cases, an increase in such mortality results in a smaller equilibrium population density of adult fish. The stability of the population with respect to perturbations about its equilibrium point is increased in these cases. However, situations can occur where a slight increase in mortality causes a catastrophic population decline. The model is used to generate autoregression graphs of population numbers that can be compared with field data. Key words: stock–recruitment, young-of-the-year mortality, compensation, Leslie matrix, mathematical model

OUTPUT FEEDBACK CONTROL FOR AN EXPLOITED STRUCTURED MODEL OF A FISHING PROBLEM

2008 ◽  
Vol 16 (01) ◽  
pp. 107-117 ◽  
Author(s):  
E. EL MAZOUDI ◽  
N. ELALAMI ◽  
M. MRABTI
Keyword(s):  
Output Feedback ◽  
Output Feedback Control ◽  
Fish Population ◽  
Fishing Effort ◽  
State Regulation ◽  
Age Classes ◽  
Trivial Equilibrium ◽  
Stability And Stabilization ◽  
The Stability ◽  
Two Stages

In this paper, the problem of global state regulation via output feedback is investigated to study a structured fishing model, in order to stabilize its states around a non-trivial equilibrium. In our case, the two stages of the juvenile and adults ages of fish population are considered. In order to apply the tools of automatic control to our model, the fishing effort is used as a control term, the age classes as a states and the quantity of captured fish per unit of effort as a measured output. A Lyapunov function is adapted to study the stability and stabilization of the studied system around the non-trivial steady states. Numerical example demonstrates the effectiveness and the convergence of the states to the equilibrium.

scholarly journals Cooperative Game for Fish Harvesting and Pollution Control

Games ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 65
Author(s):  
Mouhamadou Samsidy Goudiaby ◽  
Ben Mansour Dia ◽  
Mamadou L. Diagne ◽  
Hamidou Tembine
Keyword(s):  
Cooperative Game ◽  
Sufficient Conditions ◽  
Fish Population ◽  
Fish Growth ◽  
Fish Stock ◽  
Logistic Growth ◽  
Design Strategies ◽  
Incentive Design ◽  
Taxation Policy ◽  
The Stability

This paper studies fishery strategies in lakes, seas, and shallow rivers subject to agricultural and industrial pollution. The flowing pollutants are modeled by a nonlinear differential equation in a general manner. The logistic growth model for the fish population is modified to cover the pollution impact on the fish growth rate. We start by presenting the stability analysis of the dynamical system to discern the different types of the evolution of the fish population according to human actions. A cooperative game is formulated to design strategies for preserving the fish population by controlling the pollution as well as the fish stock for harvesting. The sufficient conditions for implementing the cooperative strategy are investigated through an incentive design approach with an adaptive taxation policy for the players. Numerical results are presented to illustrate the benefit of the cooperative for fish population preservation but also for the players’ rewards.

scholarly journals Survival analysis of a stochastic delay single-species system in polluted environment with psychological effect and pulse toxicant input

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiangjun Dai ◽  
Suli Wang ◽  
Weizhi Xiong ◽  
Ni Li
Keyword(s):  
Sufficient Conditions ◽  
Single Species ◽  
Threshold Value ◽  
Psychological Effect ◽  
Polluted Environment ◽  
Population System ◽  
Stochastic Delay ◽  
Species Population ◽  
The Mean ◽  
Single Species Population

Abstract We propose and study a stochastic delay single-species population system in polluted environment with psychological effect and pulse toxicant input. We establish sufficient conditions for the extinction, nonpersistence in the mean, weak persistence, and strong persistence of the single-species population and obtain the threshold value between extinction and weak persistence. Finally, we confirm the efficiency of the main results by numerical simulations.

On the Necessary and Sufficient Conditions for the Stability of Linear Generalized Ordinary Differential, Linear Impulsive and Linear Difference Systems

2009 ◽  
Vol 16 (4) ◽  
pp. 597-616
Author(s):  
Shota Akhalaia ◽  
Malkhaz Ashordia ◽  
Nestan Kekelia
Keyword(s):  
Linear System ◽  
Difference Equations ◽  
Closed Interval ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Difference Systems ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Generalized Ordinary Differential Equations ◽  
Lyapunov Sense

Abstract Necessary and sufficient conditions are established for the stability in the Lyapunov sense of solutions of a linear system of generalized ordinary differential equations 𝑑𝑥(𝑡) = 𝑑𝐴(𝑡) · 𝑥(𝑡) + 𝑑𝑓(𝑡), where and are, respectively, matrix- and vector-functions with bounded total variation components on every closed interval from . The results are realized for the linear systems of impulsive, ordinary differential and difference equations.

scholarly journals Stability and Hopf Bifurcation in a Delayed SEIRS Worm Model in Computer Network

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Zizhen Zhang ◽  
Huizhong Yang
Keyword(s):  
Hopf Bifurcation ◽  
Computer Network ◽  
Sufficient Conditions ◽  
Positive Equilibrium ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Local Hopf Bifurcation ◽  
Form Theory ◽  
Worm Model ◽  
The Stability

A delayed SEIRS epidemic model with vertical transmission in computer network is considered. Sufficient conditions for local stability of the positive equilibrium and existence of local Hopf bifurcation are obtained by analyzing distribution of the roots of the associated characteristic equation. Furthermore, the direction of the local Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by using the normal form theory and center manifold theorem. Finally, a numerical example is presented to verify the theoretical analysis.

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