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.

scholarly journals The Dynamics of a Food Web System: Role of a Prey Refuge Depending on Both Species

2021 ◽  
pp. 639-657
Author(s):  
Ekhlas Abd Al-Husain Jabr ◽  
Dahlia Khaled Bahlool
Keyword(s):  
Food Web ◽  
Equilibrium Points ◽  
Uniform Boundedness ◽  
Prey Refuge ◽  
Stable Point ◽  
Predator Species ◽  
Periodic Dynamics ◽  
The Web ◽  
Food Web Model

This paper aims to study the role of a prey refuge that depends on both prey and predator species on the dynamics of a food web model. It is assumed that the food transfer among the web levels occurs according to Lotka-Volterra functional response. The solution properties, such as existence, uniqueness, and uniform boundedness, are discussed. The local, as well as the global, stabilities of the solution of the system are investigated. The persistence of the system is studied with the assistance of average Lyapunov function. The local bifurcation conditions that may occur near the equilibrium points are established. Finally, numerical simulation is used to confirm our obtained results. It is observed that the system has only one type of attractors that is a stable point, while periodic dynamics do not exist even on the boundary planes.

scholarly journals Stability Analysis of Model tuberculosis Spread in Diabetes Mellitus Patients with Treatment Factors

2020 ◽  
Vol 17 (1) ◽  
pp. 50-60
Author(s):  
Nursamsi Nursamsi
Keyword(s):  
Diabetes Mellitus ◽  
Numerical Simulation ◽  
Stability Analysis ◽  
Equilibrium Point ◽  
Immune Function ◽  
Blood Sugar ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Sugar Levels ◽  
The Stability

Diabetes mellitus (Dm) is a disease associated with impaired immune function so it is more susceptible to get infections including Tuberculosis (Tb). Tb disease can also worsen blood sugar levels which can cause Dm disease. This study aims to analyze and determine the stability of the equilibrium point of the spread of Tb disease in patients with Dm with consideration nine compartments, which are susceptible Tb without Dm, susceptible Tb without Dm complication, susceptible Tb with Dm complication, expose Tb without Dm, expose Tb with Dm, infected Tb without Dm, infected Tb with Dm, recovered Tb without Dm, and recovered Tb with Dm with treatment factors. The result obtained from the analysis of the model is two equilibrium points, which are the non endemic and endemic equilibrium points. The endemic equilibrium point does not exist if , endemic will appear if . Analytical and numerical simulation show that the spread of disease can be reduced and stopped if treatment is given to the infected compartment.

A prey - partially dependent predator with a reserved zone: modelling and analysis

2015 ◽  
Vol 5 (1) ◽  
pp. 1
Author(s):  
M.V. Ramana Murthy ◽  
Dahlia Khaled
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Lyapunov Function ◽  
Functional Response ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
The Other ◽  
Local Bifurcation ◽  
Control Parameters ◽  
Persistence Conditions

<p>In this paper, a mathematical model consisting of a prey-partially dependent predator has been proposed and analyzed. It is assumed that the prey moving between two types of zones, one is assumed to be a free hunting zone that is known as an unreserved zone and the other is a reserved zone where hunting is prohibited. The predator consumes the prey according to the Beddington-DeAngelis type of functional response. The existence, uniqueness and boundedness of the solution of the system are discussed. The dynamical behavior of the system has been investigated locally as well as globally with the help of Lyapunov function. The persistence conditions of the system are established. Local bifurcation near the equilibrium points has been investigated. Finally, numerical simulation has been used to specify the control parameters and confirm the obtained results.</p>

scholarly journals ANALISIS KESTABILAN MODEL INTERAKSI PREDATOR-PREY DENGAN FUNGSI RESPON MONOD-HALDANE DAN PERILAKU ANTI PEMANGSA

2020 ◽  
Vol 8 (2) ◽  
pp. 51-59
Author(s):  
Muhammad Bachtiar Gaib ◽  
Wahdania At. Ja'a
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Predator Prey ◽  
First Case ◽  
Point Determination ◽  
Predator Model ◽  
The Stability ◽  
Predator Behavior

This article examines a competing prey-predator model using the Monod-Haldane response function and anti-predator behavior. This article discusses equilibrium point determination, equilibrium point stability analysis, and numerical simulation. Obtained three equilibrium points, namely T1, T2, and T3, where the equilibrium-point is always saddle, the stability of the equilibrium points T2 and T3 will be stable if it meets the predetermined parameter requirements. There are two cases in the equilibrium point where the first case is vertically stable and the second case is spiral stable.

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.

Bifurcation and stability of resonance of electric vehicle powertrain: Focus on the influence of electromagnetic parameters

2021 ◽  
pp. 095440702110450
Author(s):  
Qingzhen Han ◽  
Shiqin Niu ◽  
Lei He
Keyword(s):  
Electric Vehicle ◽  
Electromechanical Coupling ◽  
Equilibrium Points ◽  
Resonance Curve ◽  
Drive Shaft ◽  
Electromagnetic Parameters ◽  
Stability And Bifurcation ◽  
Fold Bifurcation ◽  
The Stability ◽  
Vehicle Powertrain

The influence of the electromagnetic parameters on the torsional dynamics of the electric vehicle powertrain is studied by considering the electromechanical coupling effect. By adding the electromagnetic torque on the drive side, the powertrain is simplified as nonlinear drive-shaft model. The number, stability, and bifurcation conditions of the equilibrium points of the nonlinear drive-shaft model are deduced. Based on the averaged equations and the amplitude-frequency response equation, the stability and bifurcation conditions, such as fold bifurcation and Hopf bifurcation, of the resonance curve are discussed. The influence of electromagnetic parameters on the torsional dynamics is studied by simulation. It is shown that with the change of the parameters, the number as well as the stability of the equilibrium points may be changed which is affected by fold bifurcation. It is also shown that the resonance curve may lose its stability when fold bifurcation happens. By limiting the parameters in the region without fold bifurcation, the unstable dynamics of the resonance curve can be controlled.

scholarly journals “Stability Analysis of Three Species Ammensalism Model with Time Delay”

2019 ◽  
Vol 8 (2S11) ◽  
pp. 3664-3670
Keyword(s):  
Numerical Simulation ◽  
Stability Analysis ◽  
Time Delay ◽  
Global Stability ◽  
Analytical Study ◽  
Present Model ◽  
Ecological Model ◽  
Equilibrium Points

The present model is devoted to an analytical study of a three species syn-ecological model which the 1 st species ( ) N1 ammensal on the 2 nd species ( ) N2 and 2 nd species ( ) N2 ammensal on the 3 rd species ( ) N3 . Here 1 st species and 2 nd species are neutral to each other. A time delay is established between 1 st species and 2 nd species and 2 nd species and 3rd species. All attainable equilibrium points of the model are known and native stability for each case is mentioned and also the global stability of co-existing state is discussed by constructing appropriate Lyapunov operate. Further, precise solutions of perturbed equations are derived. The steadiness analysis is supported by numerical simulation victimization MatLab.

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.

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