scholarly journals Persistence, extinction and global asymptotical stability of a non-autonomous predator–prey model with random perturbation

2012 ◽  
Vol 36 (11) ◽  
pp. 5344-5353 ◽  
Author(s):  
Meng Liu ◽  
Ke Wang
Keyword(s):  
Random Perturbation ◽  
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 Periodic Solution of a Neutral Delay Leslie Predator-Prey Model and the Effect of Random Perturbation on the Smith Growth Model

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15 ◽  
Author(s):  
Tongtong Li ◽  
Wencai Zhao
Keyword(s):  
Random Perturbation ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Neutral Delay ◽  
Predator Prey ◽  
Stochastic Disturbance ◽  
Predator Prey Model ◽  
Prey Model ◽  
Predator Prey Models ◽  
The Impact

This paper puts forward a class of ratio-dependent Leslie predator-prey models. Firstly, a neutral delay predator-prey model with ratio dependence and impulse control is established and the existence of positive periodic solutions is proved by the coincidence degree theory. Secondly, a stochastic disturbance Leslie model of Smith growth is obtained when the interference of white noise is taken into consideration and the impact of delay is ignored. Applying Ito^’s formula, we get the conditions of system persistence and extinction. Finally we verify the correctness of theoretical analysis with numerical simulations.

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