Multiple limit cycles and global stability in predator-prey model

1999 ◽  
Vol 15 (2) ◽  
pp. 206-219 ◽  
Author(s):  
Wang Yuquan ◽  
Jing Zhujun ◽  
K. Y. Chan
Keyword(s):  
Global Stability ◽  
Limit Cycles ◽  
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.

scholarly journals Dynamics and bifurcations of a ratio-dependent predator-prey model

2022 ◽  
Vol 40 ◽  
pp. 1-20
Author(s):  
Parisa Azizi ◽  
Reza Khoshsiar Ghaziani
Keyword(s):  
Normal Form ◽  
Limit Cycles ◽  
Numerical Continuation ◽  
Predator Prey ◽  
Bifurcation Points ◽  
Predator Prey Model ◽  
Prey Model ◽  
Ratio Dependent

In this paper, we study a ratio-dependent predator-prey model with modied Holling-Tanner formalism, by using dynamical techniques and numerical continuation algorithms implemented in Matcont. We determine codim-1 and 2 bifurcation points and their corresponding normal form coecients. We also compute a curve of limit cycles of the system emanating from a Hopf point.

Limit cycles in a generalized Gause-type predator–prey model

2008 ◽  
Vol 37 (5) ◽  
pp. 1343-1355 ◽  
Author(s):  
S.M. Moghadas ◽  
B.D. Corbett
Keyword(s):  
Limit Cycles ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey 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.

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