Conditions for Global Stability Concerning a Prey-Predator Model with Delay Effects

1979 ◽  
Vol 36 (2) ◽  
pp. 281-286 ◽  
Author(s):  
Anthony Leung
Keyword(s):  
Global Stability ◽  
Delay Effects ◽  
Predator Model

scholarly journals Fractional order prey-predator model with infected predators in the presence of competition and toxicity

2020 ◽  
Vol 15 ◽  
pp. 38
Author(s):  
M. R. Lemnaouar ◽  
M. Khalfaoui ◽  
Y. Louartassi ◽  
I. Tolaimate
Keyword(s):  
Global Stability ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Local And Global Stability ◽  
Predator Model ◽  
Reserved Area

In this paper, we propose a fractional-order prey-predator model with reserved area in the presence of the toxicity and competition. We prove different mathematical results like existence, uniqueness, non negativity and boundedness of the solution for our model. Further, we discuss the local and global stability of these equilibria. Finally, we perform numerical simulations to prove our results.

scholarly journals Global Stability Analysis and Optimal Control of a Harvested Ecoepidemiological Prey Predator Model with Vaccination and Taxation

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Chao Liu ◽  
Qingling Zhang ◽  
Jinna Li
Keyword(s):  
Optimal Control ◽  
Stability Analysis ◽  
Global Stability ◽  
Interaction Mechanism ◽  
Prey Population ◽  
Predator Population ◽  
Optimal Control Strategy ◽  
Global Stability Analysis ◽  
Selective Harvest ◽  
Predator Model

We propose an ecoepidemiological prey predator model, where selective harvest effort on predator population is considered. Vaccination and taxation are introduced as control instruments, which are utilized to control number of susceptible prey population and protect predator population from overexploitation, respectively. Conditions which influence nonnegativity and boundedness of solutions are studied. Global stability analysis around disease-free equilibrium is discussed based on robust Bendixson criterion, which is theoretically beneficial to studying coexistence and interaction mechanism of population within harvested ecoepidemiological system. By using Pontryagin’s maximum principle, an optimal control strategy is derived to maximize the total discounted net economic revenue to society as well as protect prey population from infectious disease. Numerical simulations are carried out to show the consistency with theoretical analysis.

scholarly journals The The Dynamics of a Prey-Predator Model with Infectious Disease in Prey: Role of Media Coverage

2021 ◽  
pp. 4930-4952
Author(s):  
Wassan Hussein ◽  
Huda Abdul Satar
Keyword(s):  
Infectious Disease ◽  
Global Stability ◽  
Numerical Simulations ◽  
Functional Response ◽  
Media Coverage ◽  
Epidemiological Model ◽  
Local Bifurcation ◽  
Predator Model ◽  
Disease In Prey

In this paper, an eco-epidemiological model with media coverage effect is proposed and studied. A prey-predator model with modified Leslie-Gower and functional response is studied. An  -type of disease in prey is considered.  The existence, uniqueness and boundedness of the solution of the model are discussed. The local and global stability of this system are carried out. The conditions for the persistence of all species are established. The local bifurcation in the model is studied. Finally, numerical simulations are conducted to illustrate the analytical results.

scholarly journals CONTROL OF PREY DISEASE IN STAGE STRUCTURE MODEL

2020 ◽  
Vol 25 (2) ◽  
pp. 129
Author(s):  
S. A. Wuhaib ◽  
N. F. Abd
Keyword(s):  
At Risk ◽  
Periodic Solution ◽  
Global Stability ◽  
Stage Structure ◽  
Original System ◽  
Stability Conditions ◽  
Risk Of Disease ◽  
Predator Model ◽  
Mathematica Software ◽  
Infected Prey

In this paper, a mathematical model consisting of the prey-predator model, prey is at risk of disease then become as susceptible and infected, while predator with different stage structure: immature and mature predator, the infected prey is at risk recover and harvest. The function of disease is proportionality function. At the beginning, the reasons of studying stage structure and the dynamic of nontrivial subsystems that may be lead to coexistence of these types of spices explain and by using Maple software, Jacobean matrix, Routh-Hurwitz criterion, Bendixson-Dulac criterion and Lyapunov function to prove the existence, periodic solution, local and global stability. We concluded that the survival for two preys are possible through the non-periodic solution due to the Bendixson-Dulac criterion, also the immature predator neither attack preys nor yield offspring's and die when the mature predator extinction, the global stability conditions for the original system be stretch of global stability conditions for subsystems. Finally, Mathematica software employs to describe some results in numerical simulation   http://dx.doi.org/10.25130/tjps.25.2020.040

MULTI-TEAM PREY-PREDATOR MODEL

2007 ◽  
Vol 18 (10) ◽  
pp. 1609-1617 ◽  
Author(s):  
M. F. ELETTREBY ◽  
H. El-METWALLY
Keyword(s):  
Global Stability ◽  
Local Stability ◽  
Predator Model ◽  
Team Concept

Here, we apply multi team concept to the prey-predator model. The prey teams help each other. Local stability of the system is studied. Global stability and persistence of the model without help are investigated.

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.

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