scholarly journals Global stability of a periodic Holling-Tanner predator-prey model

2018 ◽  
Vol 41 (9) ◽  
pp. 3270-3281 ◽  
Author(s):  
Benedetta Lisena
Keyword(s):  
Global Stability ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

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.

GLOBAL STABILITY OF A STAGE-STRUCTURED PREDATOR–PREY MODEL WITH MODIFIED LESLIE–GOWER AND HOLLING-TYPE II SCHEMES

2012 ◽  
Vol 05 (06) ◽  
pp. 1250057 ◽  
Author(s):  
ZHONG LI ◽  
MAOAN HAN ◽  
FENGDE CHEN
Keyword(s):  
Global Stability ◽  
Positive Equilibrium ◽  
Type Ii ◽  
Iterative Technique ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

In this paper, we consider a stage-structured predator–prey model with modified Leslie–Gower and Holling-type II schemes. Using an iterative technique, we investigate the global stability of the positive equilibrium of the system. Finally, some examples are presented to verify our main result.

scholarly journals Permanence and global stability of positive solutions of a nonautonomous discrete ratio-dependent predator-prey model

2005 ◽  
Vol 2005 (2) ◽  
pp. 135-144 ◽  
Author(s):  
Hai-Feng Huo ◽  
Wan-Tong Li
Keyword(s):  
Lyapunov Function ◽  
Global Stability ◽  
Positive Solution ◽  
Positive Solutions ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Ratio Dependent

We first give sufficient conditions for the permanence of nonautonomous discrete ratio-dependent predator-prey model. By linearization of the model at positive solutions and construction of Lyapunov function, we also obtain some conditions which ensure that a positive solution of the model is stable and attracts all positive solutions.

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