scholarly journals An Eco-Epidemiological Model Incorporating Harvesting Factors

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2179
Author(s):  
Kawa Hassan ◽  
Arkan Mustafa ◽  
Mudhafar Hama
Keyword(s):  
Equilibrium Point ◽  
Functional Response ◽  
Biological System ◽  
Numerical Verification ◽  
Interior Equilibrium ◽  
Dynamical Fluctuations ◽  
Predator Model ◽  
The Stability ◽  
Analytical Section ◽  
Predator System

The biological system relies heavily on the interaction between prey and predator. Infections may spread from prey to predators or vice versa. This study proposes a virus-controlled prey-predator system with a Crowley–Martin functional response in the prey and an SI-type in the prey. A prey-predator model in which the predator uses both susceptible and sick prey is used to investigate the influence of harvesting parameters on the formation of dynamical fluctuations and stability at the interior equilibrium point. In the analytical section, we outlined the current circumstances for all possible equilibria. The stability of the system has also been explored, and the required conditions for the model’s stability at the equilibrium point have been found. In addition, we give numerical verification for our analytical findings with the help of graphical illustrations.

scholarly journals Order and Chaos in a Prey-Predator Model Incorporating Refuge, Disease, and Harvesting

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Dahlia Khaled Bahlool ◽  
Huda Abdul Satar ◽  
Hiba Abdullah Ibrahim
Keyword(s):  
Equilibrium Points ◽  
Global Dynamics ◽  
Persistence Conditions ◽  
Local Bifurcation Analysis ◽  
Uniqueness Of The Solution ◽  
Harvesting Process ◽  
Predator Model ◽  
The Stability ◽  
Predator System ◽  
Type Ii Functional Response

In this paper, a mathematical model consisting of a prey-predator system incorporating infectious disease in the prey has been proposed and analyzed. It is assumed that the predator preys upon the nonrefugees prey only according to the modified Holling type-II functional response. There is a harvesting process from the predator. The existence and uniqueness of the solution in addition to their bounded are discussed. The stability analysis of the model around all possible equilibrium points is investigated. The persistence conditions of the system are established. Local bifurcation analysis in view of the Sotomayor theorem is carried out. Numerical simulation has been applied to investigate the global dynamics and specify the effect of varying the parameters. It is observed that the system has a chaotic dynamics.

scholarly journals Bounded finite-time stabilization of the prey – predator model via Korobov’s controllability function

2021 ◽  
Vol 21 (1) ◽  
pp. 76-87
Author(s):  
Abdon E. Choque-Rivero ◽  
◽  
Fernando Ornelas-Tellez ◽  
Keyword(s):  
Equilibrium Point ◽  
Finite Time ◽  
Control Input ◽  
Bounded Control ◽  
Physical Restriction ◽  
Simulation Results ◽  
Finite Time Stabilization ◽  
Predator Model ◽  
Control Methodology ◽  
Predator System

The problem of finite-time stabilization for a Leslie-Gower prey – predator system through a bounded control input is solved. We use Korobov’s controllability function. The trajectory of the resulting motion is ensured for fulfilling a physical restriction that prey and predator cannot achieve negative values. For this purpose, a certain ellipse depending on given data and the equilibrium point of the considered system is constructed. Simulation results show the effectiveness of the proposed control methodology.

scholarly journals Note on the Stability Property of a Cooperative System Incorporating Harvesting

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Xiangdong Xie ◽  
Fengde Chen ◽  
Yalong Xue
Keyword(s):  
Iterative Method ◽  
Equilibrium Point ◽  
Stability Property ◽  
Global Attractivity ◽  
Positive Equilibrium ◽  
Cooperative System ◽  
Cooperative Model ◽  
Interior Equilibrium ◽  
The Stability

The stability of a kind of cooperative model incorporating harvesting is revisited in this paper. By using an iterative method, the global attractivity of the interior equilibrium point of the system is investigated. We show that the condition which ensures the existence of a unique positive equilibrium is enough to ensure the global attractivity of the positive equilibrium. Our results significantly improve the corresponding results of Wei and Li (2013).

Harvesting Analysis of a Predator-Prey System with Functional Response

2013 ◽  
Vol 805-806 ◽  
pp. 1957-1961
Author(s):  
Ting Wu
Keyword(s):  
Numerical Simulation ◽  
Equilibrium Point ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Optimal Harvesting ◽  
Predator Prey ◽  
Optimal Harvesting Policy ◽  
Prey System ◽  
The Stability ◽  
Maximal Principle

In this paper, a predator-prey system with functional response is studied,and a set of sufficient conditions are obtained for the stability of equilibrium point of the system. Moreover, optimal harvesting policy is obtained by using the maximal principle,and numerical simulation is applied to illustrate the correctness.

Prey–predator model for optimal harvesting with functional response incorporating prey refuge

2015 ◽  
Vol 09 (01) ◽  
pp. 1650014 ◽  
Author(s):  
G. S. Mahapatra ◽  
P. Santra
Keyword(s):  
Functional Response ◽  
System Parameter ◽  
Optimal Harvesting ◽  
Functional Responses ◽  
Prey Refuge ◽  
Numerical Examples ◽  
Pictorial Presentation ◽  
Constant Form ◽  
Predator Model ◽  
Predator System

This paper presents a prey–predator model considering the predator interacting with non-refuges prey by class of functional responses. Here we also consider harvesting for only non-refuges prey. We discuss the equilibria of the model, and their stability for hiding prey either in constant form or proportional to the densities of prey population. We also investigate various possibilities of bionomic equilibrium and optimal harvesting policy. Finally we present numerical examples with pictorial presentation of the various effects of the prey–predator system parameter.

scholarly journals Dynamical Analysis of a Class of Prey-Predator Model with Beddington-DeAngelis Functional Response, Stochastic Perturbation, and Impulsive Toxicant Input

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-18 ◽  
Author(s):  
Feifei Bian ◽  
Wencai Zhao ◽  
Yi Song ◽  
Rong Yue
Keyword(s):  
Periodic Solutions ◽  
Functional Response ◽  
Regime Switching ◽  
Sufficient Conditions ◽  
Stochastic Perturbation ◽  
Dynamical Analysis ◽  
Positive Periodic Solutions ◽  
Noise Perturbation ◽  
Predator Model ◽  
Predator System

A stochastic prey-predator system in a polluted environment with Beddington-DeAngelis functional response is proposed and analyzed. Firstly, for the system with white noise perturbation, by analyzing the limit system, the existence of boundary periodic solutions and positive periodic solutions is proved and the sufficient conditions for the existence of boundary periodic solutions and positive periodic solutions are derived. And then for the stochastic system, by introducing Markov regime switching, the sufficient conditions for extinction or persistence of such system are obtained. Furthermore, we proved that the system is ergodic and has a stationary distribution when the concentration of toxicant is a positive constant. Finally, two examples with numerical simulations are carried out in order to illustrate the theoretical results.

STABILITY ANALYSIS OF A PREY-PREDATOR MODEL WITH DELAY AND HARVESTING

2004 ◽  
Vol 12 (01) ◽  
pp. 61-71 ◽  
Author(s):  
TAPAN KUMAR KAR
Keyword(s):  
Stability Analysis ◽  
Computer Simulations ◽  
Significant Role ◽  
Combined Effects ◽  
Predator Model ◽  
The Stability ◽  
Predator System

An analysis is presented for a model of a two species prey-predator system subject to the combined effects of delay and harvesting. Our study shows that, both the delay and harvesting effort may play a significant role on the stability of the system. Computer simulations are carried out to explain some of the mathematical conclusions.

DYNAMICAL BEHAVIOR IN A HARVESTED DIFFERENTIAL-ALGEBRAIC PREY-PREDATOR MODEL

2009 ◽  
Vol 02 (04) ◽  
pp. 463-482 ◽  
Author(s):  
CHAO LIU ◽  
QINGLING ZHANG ◽  
XUE ZHANG ◽  
XIAODONG DUAN
Keyword(s):  
Bifurcation Theory ◽  
State Feedback ◽  
Dynamical Behavior ◽  
Algebraic Model ◽  
Economic Interest ◽  
Interior Equilibrium ◽  
Proposed Model ◽  
Differential Algebraic System ◽  
Predator Model ◽  
Predator System

A differential-algebraic model which considers a prey-predator system with harvest effort on predator is proposed. By using the differential-algebraic system theory and bifurcation theory, local stability of the proposed model around the interior equilibrium is investigated. Furthermore, the instability mechanism of the proposed model due to the variation of economic interest of harvesting is studied. With the purpose of stabilizing the proposed model around the interior equilibrium and maintaining the economic interest of harvesting at an ideal level, a state feedback controller is designed. Finally, numerical simulations are carried out to show the consistency with theoretical analysis.

scholarly journals Bifurcation Analysis of a Delayed Predator-Prey Model with Holling Type III Functional Response and Predator Harvesting

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Uttam Das ◽  
T. K. Kar
Keyword(s):  
Hopf Bifurcation ◽  
Functional Response ◽  
Normal Form Theory ◽  
Predator Species ◽  
Center Manifold Theorem ◽  
Type Iii ◽  
Predator Prey Model ◽  
Form Theory ◽  
Predator Model ◽  
The Stability

This paper tries to highlight a delayed prey-predator model with Holling type III functional response and harvesting to predator species. In this context, we have discussed local stability of the equilibria, and the occurrence of Hopf bifurcation of the system is examined by considering the harvesting effort as bifurcation parameter along with the influences of harvesting effort of the system when time delay is zero. Direction of Hopf bifurcation and the stability of bifurcating periodic solutions are also studied by applying the normal form theory and the center manifold theorem. Lastly some numerical simulations are carried out to draw for the validity of the theoretical results.

Dynamics of an Innovation Diffusion Model with Time Delay

2017 ◽  
Vol 7 (3) ◽  
pp. 455-481 ◽  
Author(s):  
Rakesh Kumar ◽  
Anuj K. Sharma ◽  
Kulbhushan Agnihotri
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Population Density ◽  
Differential Equations ◽  
Equilibrium Point ◽  
Innovation Diffusion ◽  
Critical Value ◽  
Normal Form Theory ◽  
Interior Equilibrium ◽  
The Stability

AbstractA nonlinear mathematical model for innovation diffusion is proposed. The system of ordinary differential equations incorporates variable external influences (the cumulative density of marketing efforts), variable internal influences (the cumulative density of word of mouth) and a logistically growing human population (the variable potential consumers). The change in population density is due to various demographic processes such as intrinsic growth rate, emigration, death rate etc. Thus the problem involves two dynamic variables viz. a non-adopter population density and an adopter population density. The model is analysed qualitatively using the stability theory of differential equations, with the help of the corresponding characteristic equation of the system. The interior equilibrium point can be stable for all time delays to a critical value, beyond which the system becomes unstable and a Hopf bifurcation occurs at a second critical value. Employing normal form theory and a centre manifold theorem applicable to functional differential equations, we derive some explicit formulas determining the stability, the direction and other properties of the bifurcating periodic solutions. Our numerical simulations show that the system behaviour can become extremely complicated as the time delay increases, with a stable interior equilibrium point leading to a limit cycle with one local maximum and minimum per cycle (Hopf bifurcation), then limit cycles with more local maxima and minima per cycle, and finally chaotic solutions.

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