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 The Dynamics of A Square Root Prey-Predator Model with Fear

2020 ◽  
pp. 139-146
Author(s):  
Nabaa Hassain Fakhry ◽  
Raid Kamel Naji
Keyword(s):  
Ecological Model ◽  
Equilibrium Points ◽  
Global Dynamics ◽  
Local Bifurcation ◽  
Square Root ◽  
Predator Species ◽  
Local Bifurcation Analysis ◽  
Predator Model ◽  
The Stability ◽  
Predator System

An ecological model consisting of prey-predator system involving the prey’s fear is proposed and studied. It is assumed that the predator species consumed the prey according to prey square root type of functional response. The existence, uniqueness and boundedness of the solution are examined. All the possible equilibrium points are determined. The stability analysis of these points is investigated along with the persistence of the system. The local bifurcation analysis is carried out. Finally, this paper is ended with a numerical simulation to understand the global dynamics of the system.

scholarly journals The Effects of Media Coverage on the Dynamics of Disease in Prey-Predator Model

2021 ◽  
pp. 981-996
Author(s):  
Walaa Madhat Alwan ◽  
Huda Abdul Satar
Keyword(s):  
Media Coverage ◽  
Global Dynamics ◽  
Local Bifurcation ◽  
Persistence Conditions ◽  
Proposed Model ◽  
Disease In Predator ◽  
Predator Model ◽  
The Stability ◽  
Effects Of Media ◽  
Disease In Prey

In this paper, an eco-epidemiological model with media coverage effects is established and studied. An -type of disease in predator is considered.  All the properties of the solution of the proposed model are discussed. An application to the stability theory was carried out to investigate the local as well as global stability of the system. The persistence conditions of the model are determined. The occurrence of local bifurcation in the model is studied. Further investigation of the global dynamics of the model is achieved through using a numerical simulation.

A STUDY OF BIFURCATION OF PREY–PREDATOR MODEL WITH TIME DELAY AND HARVESTING USING FUZZY PARAMETERS

2018 ◽  
Vol 26 (02) ◽  
pp. 339-372 ◽  
Author(s):  
D. PAL ◽  
G. S. MAHAPATRA ◽  
G. P. SAMANTA
Keyword(s):  
Time Delay ◽  
Equilibrium Points ◽  
Fuzzy Model ◽  
Solution Procedure ◽  
Distance Method ◽  
Gestation Delay ◽  
Fuzzy Environment ◽  
Predator Model ◽  
The Stability ◽  
Predator System

In this work, a fuzzy prey–predator system with time delay is proposed. The model consists of two preys and one predator. The biological coefficients/parameters are considered as imprecise in nature and quantified by triangular fuzzy numbers. We have studied the effect of gestation delay on the stability of the system in fuzzy environment. The signed distance method for the defuzzification of the proposed fuzzy prey–predator system is adopted. For the underlying fuzzy model, we have provided a solution procedure to find all possible equilibrium points and studied their stabilities in the fuzzy sense. It is observed that there are stability switches, and Hopf-bifurcation occurs when the delay crosses some critical value in fuzzy sense. Numerical illustrations are provided in crisp as well as fuzzy environment with the help of graphical presentations to support our proposed approach.

scholarly journals A Study of a Diseased Prey-Predator Model with Refuge in Prey and Harvesting from Predator

2018 ◽  
Vol 2018 ◽  
pp. 1-17 ◽  
Author(s):  
Ahmed Sami Abdulghafour ◽  
Raid Kamel Naji
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Equilibrium Points ◽  
Nonlinear Ordinary Differential Equations ◽  
First Order ◽  
Persistence Conditions ◽  
System Solution ◽  
Predator Model ◽  
Predator System ◽  
Infected Prey

In this paper, a mathematical model of a prey-predator system with infectious disease in the prey population is proposed and studied. It is assumed that there is a constant refuge in prey as a defensive property against predation and harvesting from the predator. The proposed mathematical model is consisting of three first-order nonlinear ordinary differential equations, which describe the interaction among the healthy prey, infected prey, and predator. The existence, uniqueness, and boundedness of the system’ solution are investigated. The system's equilibrium points are calculated with studying their local and global stability. The persistence conditions of the proposed system are established. Finally the obtained analytical results are justified by a numerical simulation.

Stability and Hopf Bifurcation of a Delayed Prey–Predator Model with Disease in the Predator

2019 ◽  
Vol 29 (07) ◽  
pp. 1950091 ◽  
Author(s):  
Chuangxia Huang ◽  
Hua Zhang ◽  
Jinde Cao ◽  
Haijun Hu
Keyword(s):  
Hopf Bifurcation ◽  
Equilibrium Points ◽  
Mass Action ◽  
Functional Responses ◽  
Predator Species ◽  
Interior Equilibrium ◽  
Positivity Of Solutions ◽  
Predator Model ◽  
The Stability ◽  
Type Ii Functional Response

Dealing with the epidemiological prey–predator is very important for us to understand the dynamical characteristics of population models. The existing literature has shown that disease introduction into the predator group can destabilize the established prey–predator communities. In this paper, we establish a new delayed SIS epidemiological prey–predator model with the assumptions that the disease is transmitted among the predator species only and different type of predators have different functional responses, viz. the infected predator consumes the prey according to Holling type-II functional response and the susceptible predator consumes the prey following the law of mass action. The positivity of solutions, the existence of various equilibrium points, the stability and bifurcation at those equilibrium points are investigated at length. Using the incubation period as bifurcation parameter, it is observed that a Hopf bifurcation may occur around the equilibrium points when the parameter passes through some critical values. We also discuss the direction and stability of the Hopf bifurcation around the interior equilibrium point. Simulations are arranged to show the correctness and effectiveness of these theoretical results.

scholarly journals Stability and Bifurcation of a Prey-Predator-Scavenger Model in the Existence of Toxicant and Harvesting

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Huda Abdul Satar ◽  
Raid Kamel Naji
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Food Web ◽  
Equilibrium Points ◽  
Local Bifurcation ◽  
Persistence Conditions ◽  
Stability And Bifurcation ◽  
Periodic Dynamics ◽  
The Stability ◽  
Food Web Model

In this paper a prey-predator-scavenger food web model is proposed and studied. It is assumed that the model considered the effect of harvesting and all the species are infected by some toxicants released by some other species. The stability analysis of all possible equilibrium points is discussed. The persistence conditions of the system are established. The occurrence of local bifurcation around the equilibrium points is investigated. Numerical simulation is used and the obtained solution curves are drawn to illustrate the results of the model. Finally, the nonexistence of periodic dynamics is discussed analytically as well as numerically.

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.

scholarly journals A Prey-Predator Model with Michael Mentence Type of Predator Harvesting and Infectious Disease in Prey

2020 ◽  
pp. 1146-1163
Author(s):  
Hiba Abdullah Ibrahim ◽  
Raid Kamel Naji
Keyword(s):  
Infectious Disease ◽  
Numerical Simulations ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Local Bifurcation ◽  
Persistence Conditions ◽  
Analytical Results ◽  
Predator Model ◽  
Disease In Prey

A prey-predator model with Michael Mentence type of predator harvesting and infectious disease in prey is studied. The existence, uniqueness and boundedness of the solution of the model are investigated. The dynamical behavior of the system is studied locally as well as globally. The persistence conditions of the system are established. Local bifurcation near each of the equilibrium points is investigated. Finally, numerical simulations are given to show our obtained analytical results.

scholarly journals A prey-predator model with infection in both prey and predator

Filomat ◽  
2015 ◽  
Vol 29 (8) ◽  
pp. 1753-1767 ◽  
Author(s):  
S.P. Bera ◽  
A. Maiti ◽  
G.P. Samanta
Keyword(s):  
Differential Equation ◽  
Computer Simulations ◽  
Equilibrium Points ◽  
Predator Model ◽  
Predator System

This paper aims to study the dynamical behaviours of a prey-predator system where both prey and predator populations are affected by diseases. A system of four differential equation has been proposed and analyzed. Stability of the equilibrium points of the model has been investigated. Computer simulations are carried out to illustrate our analytical findings. The biological implications of analytical and numerical findings are discussed critically.

scholarly journals The Dynamical Analysis of a Prey-Predator Model with a Refuge-Stage Structure Prey Population

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Raid Kamel Naji ◽  
Salam Jasim Majeed
Keyword(s):  
Mathematical Model ◽  
Equilibrium Points ◽  
Stage Structure ◽  
Dynamical Analysis ◽  
Local Bifurcation ◽  
Structure Population ◽  
Global Stability Analysis ◽  
Proposed Model ◽  
Predator Model ◽  
Predator System

We proposed and analyzed a mathematical model dealing with two species of prey-predator system. It is assumed that the prey is a stage structure population consisting of two compartments known as immature prey and mature prey. It has a refuge capability as a defensive property against the predation. The existence, uniqueness, and boundedness of the solution of the proposed model are discussed. All the feasible equilibrium points are determined. The local and global stability analysis of them are investigated. The occurrence of local bifurcation (such as saddle node, transcritical, and pitchfork) near each of the equilibrium points is studied. Finally, numerical simulations are given to support the analytic results.

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