Global asymptotical stability of a dimensional Leslie–Gower predator–prey model

2014 ◽  
Vol 235 ◽  
pp. 377-382
Author(s):  
Wensheng Yang ◽  
Xuepeng Li
Keyword(s):  
Asymptotical Stability ◽  
Global Asymptotical Stability ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

Analysis of a Predator–Prey Model with Sparssing Effect

2014 ◽  
Vol 971-973 ◽  
pp. 2234-2237
Author(s):  
Yong Po Zhang ◽  
Ming Juan Ma ◽  
Yue Shuang ◽  
Jia Hui Sun
Keyword(s):  
Sufficient Conditions ◽  
Liapunov Function ◽  
Latent Root ◽  
Asymptotical Stability ◽  
Positive Equilibrium ◽  
Effect Analysis ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Boundary Equilibrium

In this paper we formulated and analyzed a predator-prey model with sparssing effect, analysis of the existing conditions of equilibrium point, and the sufficient condition of the local asymptotical stability of the equilibrium was studied with the method of latent root, and furthermore, by constructing a Liapunov function to get the boundary equilibrium and the positive equilibrium sufficient conditions for the globally asymptotical stability.

DYNAMICS OF A DIFFUSIVE PREDATOR–PREY MODEL WITH ADDITIVE ALLEE EFFECT

2012 ◽  
Vol 05 (02) ◽  
pp. 1250023 ◽  
Author(s):  
YONGLI CAI ◽  
WEIMING WANG ◽  
JINFENG WANG
Keyword(s):  
Allee Effect ◽  
Dynamical Behavior ◽  
Positive Equilibrium ◽  
Global Asymptotical Stability ◽  
Allee Effects ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Prey Model ◽  
Holling Ii Functional Response

In this paper, we investigate the dynamics of a diffusive predator–prey model with Holling-II functional response and the additive Allee effect in prey. We show the local and global asymptotical stability of the positive equilibrium, and give the conditions of the existence of the Hopf bifurcation. By carrying out global qualitative and bifurcation analysis, it is shown that the weak and strong Allee effects in prey can induce different dynamical behavior in the predator–prey model. Furthermore, we use some numerical simulations to illustrate the dynamics of the model. The results may be helpful for controlling and managing the predator–prey system.

scholarly journals Dynamics of Stage-Structured Predator–Prey Model with Beddington–DeAngelis Functional Response and Harvesting

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2169
Author(s):  
Haiyin Li ◽  
Xuhua Cheng
Keyword(s):  
Functional Response ◽  
Local Stability ◽  
Asymptotical Stability ◽  
Positive Equilibrium ◽  
Global Asymptotical Stability ◽  
Globally Asymptotically Stable ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Boundary Equilibrium ◽  
The Stability

In this paper, we investigate the stability of equilibrium in the stage-structured and density-dependent predator–prey system with Beddington–DeAngelis functional response. First, by checking the sign of the real part for eigenvalue, local stability of origin equilibrium and boundary equilibrium are studied. Second, we explore the local stability of the positive equilibrium for τ=0 and τ≠0 (time delay τ is the time taken from immaturity to maturity predator), which shows that local stability of the positive equilibrium is dependent on parameter τ. Third, we qualitatively analyze global asymptotical stability of the positive equilibrium. Based on stability theory of periodic solutions, global asymptotical stability of the positive equilibrium is obtained when τ=0; by constructing Lyapunov functions, we conclude that the positive equilibrium is also globally asymptotically stable when τ≠0. Finally, examples with numerical simulations are given to illustrate the obtained results.

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