Dynamic Properties of the Predator–Prey Discontinuous Dynamical System

2012 ◽  
Vol 67 (1-2) ◽  
pp. 57-60 ◽  
Author(s):  
Ahmed M. A. El-Sayed ◽  
Mohamed E. Nasr
Keyword(s):  
Dynamical System ◽  
Global Stability ◽  
Existence And Uniqueness ◽  
Dynamic Properties ◽  
Equilibrium Points ◽  
Stable Solution ◽  
Predator Prey ◽  
Local And Global Stability ◽  
Discontinuous Dynamical System

In this work, we study the dynamic properties (equilibrium points, local and global stability, chaos and bifurcation) of the predator-prey discontinuous dynamical system. The existence and uniqueness of uniformly Lyapunov stable solution will be proved

scholarly journals Dynamic Properties of the Fractional-Order Logistic Equation of Complex Variables

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
A. M. A. El-Sayed ◽  
E. Ahmed ◽  
H. A. A. El-Saka
Keyword(s):  
Dynamical System ◽  
Global Stability ◽  
Fractional Order ◽  
Existence And Uniqueness ◽  
Dynamic Properties ◽  
Equilibrium Points ◽  
Stable Solution ◽  
Complex Variables ◽  
Logistic Equation ◽  
Local And Global Stability

We study the dynamic properties (equilibrium points, local and global stability, chaos and bifurcation) of the continuous dynamical system of the logistic equation of complex variables. The existence and uniqueness of uniformly Lyapunov stable solution will be proved.

Asymptotic Behavior of the Fractional Order three Species Prey–Predator Model

2018 ◽  
Vol 19 (7-8) ◽  
pp. 721-733 ◽  
Author(s):  
M. Sambath ◽  
P. Ramesh ◽  
K. Balachandran
Keyword(s):  
Dynamical System ◽  
Asymptotic Behavior ◽  
Global Stability ◽  
Fractional Order ◽  
Equilibrium Points ◽  
Numerical Results ◽  
Predator Prey ◽  
Local And Global Stability ◽  
Predator Prey Model ◽  
Predator Model

AbstractIn this work, we introduce fractional order predator–prey model with infected predator. First, we prove different mathematical results like existence, uniqueness, non-negativity and boundedness of the solutions of fractional order dynamical system. Further, we investigate the local and global stability of all feasible equilibrium points of the system. Numerical results are illustrated as several examples.

scholarly journals The Stability of Gauss Model Having One-Prey and Two-Predators

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
A. Farajzadeh ◽  
M. H. Rahmani Doust ◽  
F. Haghighifar ◽  
D. Baleanu
Keyword(s):  
Mathematical Biology ◽  
Global Stability ◽  
Equilibrium Points ◽  
Predator Prey ◽  
Local And Global Stability ◽  
Stability Properties ◽  
Interacting Species ◽  
Predator Prey Models ◽  
The Stability

The study of the dynamics of predator-prey interactions can be recognized as a major issue in mathematical biology. In the present paper, some Gauss predator-prey models in which three ecologically interacting species have been considered and the behavior of their solutions in the stability aspect have been investigated. The main aim of this paper is to consider the local and global stability properties of the equilibrium points for represented systems. Finally, stability of some examples of Gauss model with one prey and two predators is discussed.

scholarly journals Dynamics of a Predator–Prey Model with the Effect of Oscillation of Immigration of the Prey

Diversity ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 23
Author(s):  
Jawdat Alebraheem
Keyword(s):  
Global Stability ◽  
Stability Conditions ◽  
Dynamic Behaviors ◽  
Predator Prey ◽  
Local And Global Stability ◽  
Predator Prey Model ◽  
Prey Model ◽  
Proposed Model

In this article, the use of predator-dependent functional and numerical responses is proposed to form an autonomous predator–prey model. The dynamic behaviors of this model were analytically studied. The boundedness of the proposed model was proven; then, the Kolmogorov analysis was used for validating and identifying the coexistence and extinction conditions of the model. In addition, the local and global stability conditions of the model were determined. Moreover, a novel idea was introduced by adding the oscillation of the immigration of the prey into the model which forms a non-autonomous model. The numerically obtained results display that the dynamic behaviors of the model exhibit increasingly stable fluctuations and an increased likelihood of coexistence compared to the autonomous model.

scholarly journals Mathematical Model for Impact of Media on Cleanliness Drive in India

2018 ◽  
Vol 7 (1) ◽  
pp. 29-36
Author(s):  
N H Shah ◽  
J S Patel ◽  
F A Thakkar ◽  
M H Satia
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Lyapunov Function ◽  
Global Stability ◽  
Transfer Rate ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Local And Global Stability

A mathematical model on cleanliness drive in India is analysed for active cleaners and passive cleaners. Cleanliness and endemic equilibrium points are found. Local and global stability of these equilibrium points are discussed using Routh-Hurwitz criteria and Lyapunov function respectively. Impact of media (as a control) is studied on passive cleaners to become active. Numerical simulation of the model is carried out which indicates that with the help of media transfer rate to active cleaners from passive cleaners is higher.

Controlling Asthma Due to Air Pollution

2020 ◽  
pp. 1-22
Author(s):  
Ankush H. Suthar ◽  
Purvi M. Pandya
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Air Pollution ◽  
Control Theory ◽  
Global Stability ◽  
Optimal Control Theory ◽  
Positive Impact ◽  
Equilibrium Points ◽  
Local And Global Stability ◽  
Number Of Individuals

The health of our respiratory systems is directly affected by the atmosphere. Nowadays, eruption of respiratory disease and malfunctioning of lung due to the presence of harmful particles in the air is one of the most sever challenge. In this chapter, association between air pollution-related respiratory diseases, namely dyspnea, cough, and asthma, is analysed by constructing a mathematical model. Local and global stability of the equilibrium points is proved. Optimal control theory is applied in the model to optimize stability of the model. Applied optimal control theory contains four control variables, among which first control helps to reduce number of individuals who are exposed to air pollutants and the remaining three controls help to reduce the spread and exacerbation of asthma. The positive impact of controls on the model and intensity of asthma under the influence of dyspnea and cough is observed graphically by simulating the model.

Stability analysis in prey–predator system with mixed functional response

2016 ◽  
Vol 13 (4) ◽  
pp. 364-369
Author(s):  
V. Madhusudanan ◽  
S. Vijaya
Keyword(s):  
Global Stability ◽  
Numerical Simulations ◽  
Functional Response ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Type I ◽  
Content Type ◽  
Local And Global Stability ◽  
Interior Equilibrium ◽  
Predator System

Purpose This paper aims to propose and analyse a two-prey–one-predator system with mixed functional response. Design/methodology/approach The predator exhibits Holling type IV functional response to one prey and Holling type I response to other. The occurrence of various positive equilibrium points with feasibility conditions are determined. The local and global stability of interior equilibrium points are examined. The boundedness of system is analysed. The sufficient conditions for persistence of the system is obtained by using Bendixson–Dulac criteria. Numerical simulations are carried out to illustrate the analytical findings. Findings The authors have derived the local and global stability condition of interior equilibrium of the system. Originality/value The authors observe that the critical values of some system parameter undergo Hopf bifurcation around some selective equilibrium. Hence, numerical simulations reveal the condition for the system to be stable and oscillatory.

LOCAL AND GLOBAL STABILITY OF SWITCHING REGULATORS

1995 ◽  
Vol 05 (03) ◽  
pp. 305-315 ◽  
Author(s):  
HENRY CHUNG ◽  
ADRIAN IOINOVICI
Keyword(s):  
Global Stability ◽  
Closed Loop ◽  
Equilibrium Points ◽  
Stability Study ◽  
Large Signal ◽  
Time Model ◽  
Local And Global Stability ◽  
Boost Regulator ◽  
Switching Regulators ◽  
Conduction Mode

A discrete-time model of closed-loop PWM regulators is derived to describe their dynamic behavior. No small-ripple approximations are required. The same model serves both local and global stability study: by discarding the nonlinear terms and using the z-transform, stability for small-signal perturbations is checked; by keeping the nonlinear terms (products of disturbances) and using the state-plane portrait, in which equilibrium points are located, stability for large-signal perturbations is studied. The theory is applied to a multiple feedback boost regulator operating in continuous conduction mode. Its local/global stability/instability for different values of the feedback gains is determined based on the new method.

scholarly journals Limit cycles in a Kolmogorov-type model

1990 ◽  
Vol 13 (3) ◽  
pp. 555-566 ◽  
Author(s):  
Xun-Cheng Huang
Keyword(s):  
Limit Cycles ◽  
Existence And Uniqueness ◽  
Equilibrium Points ◽  
Type Model ◽  
Kolmogorov Type ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Stability Of Equilibrium ◽  
Uniqueness Of Limit Cycles ◽  
The Stability

In this paper, a Kolmogorov-type model, which includes the Gause-type model (Kuang and Freedman, 1988), the general predator-prey model (Huang 1988, Huang and Merrill 1989), and many other specialized models, is studied. The stability of equilibrium points, the existence and uniqueness of limit cycles in the model are proved.

scholarly journals Analysis of the Dynamics of SI-SI-SEIR Avian Influenza A(H7N9) Epidemic Model with Re-infection

2020 ◽  
pp. 43-73
Author(s):  
Oluwafemi I. Bada ◽  
Abayomi S. Oke ◽  
Winfred N. Mutuku ◽  
Patrick O. Aye
Keyword(s):  
Mathematical Model ◽  
Avian Influenza ◽  
Global Stability ◽  
Numerical Simulations ◽  
Epidemic Model ◽  
Influenza A ◽  
Equilibrium Points ◽  
Local And Global Stability ◽  
Continuous Contact ◽  
Non Linear

The spread of Avian influenza in Asia, Europe and Africa ever since its emergence in 2003, has been endemic in many countries. In this study, a non-linear SI-SI-SEIR Mathematical model with re-infection as a result of continuous contact with both infected poultry from farm and market is proposed. Local and global stability of the three equilibrium points are established and numerical simulations are used to validate the results.

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