scholarly journals The logistic modeling population: Having harvesting factor

2015 ◽  
Vol 25 (1) ◽  
pp. 107-115 ◽  
Author(s):  
Doust Rahmani ◽  
M. Saraj
Keyword(s):  
Phase Diagram ◽  
Equilibrium Points ◽  
First Integral ◽  
Single Species ◽  
Integral Solution ◽  
Logistic Equation ◽  
Solution Curve ◽  
Logistic Modeling ◽  
Real Model ◽  
The Stability

The present paper deals with the logistic equation having harvesting factor, which is studied in two cases, constant and non-constant. In fact, the nature of equilibrium points and solutions behavior has been analyzed for both of the above cases by finding the first integral, solution curve and phase diagram. Finally, a theorem which is describing the stability of a real model of single species is proved.

scholarly journals A Three Species Ecological Model with a Prey, Predator and Competitor to the Predator and Optimal Harvesting of the Prey

2012 ◽  
Vol 1 ◽  
pp. 21-32
Author(s):  
A.V. Papa Rao ◽  
K. Lakshmi Narayan ◽  
Shahnaz Bathul
Keyword(s):  
Ecological Model ◽  
Equilibrium Points ◽  
Single Species ◽  
Analytical Investigation ◽  
Optimal Harvesting ◽  
Stability Criteria ◽  
Linear Ordinary Differential Equations ◽  
First Order ◽  
Analytical Stability ◽  
The Stability

The present paper is devoted to an analytical investigation of three species ecological model with a Prey (N1), a predator (N2) and a competitor (N3) to the Predator without effecting the prey (N1). in addition to that, the species are provided with alternative food. The model is characterized by a set of first order non-linear ordinary differential equations. All the eight equilibrium points of the model are identified and local and global stabilitycriteria for the equilibrium states except fully washed out and single species existence are discussed. Further exact solutions of perturbed equations have been derived. The analytical stability criteria are supported by numerical simulations using mat lab. Further we discussed the effect of optimal harvesting on the stability.

scholarly journals Mathematical Analysis of a Single-Species Population Model in a Polluted Environment with Discrete Time Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-18 ◽  
Author(s):  
Swarnali Sharma ◽  
G. P. Samanta
Keyword(s):  
Hopf Bifurcation ◽  
Population Model ◽  
Time Delays ◽  
Equilibrium Points ◽  
Single Species ◽  
Polluted Environment ◽  
Normal Form Theory ◽  
Species Population ◽  
The Stability ◽  
Single Species Population

We have discussed the dynamical behaviour of a single-species population model in a polluted environment which describes the effect of toxicants on ecological system. Boundedness, positivity, and stability analysis of the model at various equilibrium points is discussed thoroughly. We have also studied the effect of single discrete delay as well as double discrete delays on the population model. Existence conditions of the Hopf bifurcation for single time delay are investigated. The length of delay preserving the stability is also estimated. The direction and the stability criteria of the bifurcating periodic solutions are determined by using the normal form theory and the center manifold theorem. The stability of the model with double time delays is investigated by using the Nyquist criteria. By choosing one of the delays as a bifurcation parameter, the model is found to undergo a Hopf bifurcation. Some numerical simulations for justifying the theoretical results are also illustrated by using MATLAB, which shows the reliability of our model from the practical point of view.

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 stability and electronic and photocatalytic properties of the ZnWO4 (010) surface determined from first-principles and thermodynamic calculations

RSC Advances ◽  
2021 ◽  
Vol 11 (38) ◽  
pp. 23477-23490
Author(s):  
Yonggang Wu ◽  
Jihua Zhang ◽  
Bingwei Long ◽  
Hong Zhang
Keyword(s):  
Phase Diagram ◽  
Density Functional Theory ◽  
First Principles ◽  
Density Functional ◽  
Thermodynamic Calculations ◽  
Photocatalytic Properties ◽  
Thermodynamic Approach ◽  
Functional Theory ◽  
Stability Phase Diagram ◽  
The Stability

The ZnWO4 (010) surface termination stability is studied using a density functional theory-based thermodynamic approach. The stability phase diagram shows that O-Zn, DL-W, and DL-Zn terminations of ZnWO4 (010) can be stabilized.

scholarly journals Nonlinear Dynamics of a PI Hydroturbine Governing System with Double Delays

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Hongwei Luo ◽  
Jiangang Zhang ◽  
Wenju Du ◽  
Jiarong Lu ◽  
Xinlei An
Keyword(s):  
Hopf Bifurcation ◽  
Equilibrium Points ◽  
Bifurcation Theorem ◽  
Center Manifold Theorem ◽  
Governing System ◽  
Normal Form Method ◽  
The Stability ◽  
System Frequency ◽  
Realistic Significance ◽  
Theoretical Results

A PI hydroturbine governing system with saturation and double delays is generated in small perturbation. The nonlinear dynamic behavior of the system is investigated. More precisely, at first, we analyze the stability and Hopf bifurcation of the PI hydroturbine governing system with double delays under the four different cases. Corresponding stability theorem and Hopf bifurcation theorem of the system are obtained at equilibrium points. And then the stability of periodic solution and the direction of the Hopf bifurcation are illustrated by using the normal form method and center manifold theorem. We find out that the stability and direction of the Hopf bifurcation are determined by three parameters. The results have great realistic significance to guarantee the power system frequency stability and improve the stability of the hydropower system. At last, some numerical examples are given to verify the correctness of the theoretical results.

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.

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.

Numerical Investigation of the Influence of Friction Coefficient on Brake Groan

2010 ◽  
Vol 44-47 ◽  
pp. 1923-1927 ◽  
Author(s):  
Xian Jie Meng
Keyword(s):  
Nonlinear Dynamics ◽  
Friction Coefficient ◽  
Degrees Of Freedom ◽  
Equilibrium Points ◽  
Static Friction ◽  
Kinetic Friction ◽  
Dynamics Model ◽  
Excited Vibration ◽  
Nonlinear Dynamics Model ◽  
The Stability

A two degrees of freedom nonlinear dynamics model of self-excited vibration induced by dry-friction of brake disk and pads is built firstly, the stability of vibration system at the equilibrium points is analyzed using the nonlinear dynamics theory. Finally the numerical method is taken to study the impacts of friction coefficient on brake groan. The calculation result shows that with the increase of kinetic friction coefficient /or the decrease of difference value between static friction coefficient and kinetic friction coefficient can prevent or restrain self-excited vibration from happening.

scholarly journals A new approach to the logistic modeling population having harvesting factor

2016 ◽  
Vol 26 (3) ◽  
pp. 381-392
Author(s):  
Chao-Pao Ho ◽  
Che-Hao Lin
Keyword(s):  
Logistic Equation ◽  
New Approach ◽  
Logistic Modeling

The present paper deals with the logistic equation having harvesting factor by a new approach. This approach is an attempt to sketch the solutions to the model Rahmani Doust and Saraj (1).

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