Stability and global Hopf bifurcation in a Leslie–Gower predator-prey model with stage structure for prey

2018 ◽  
Vol 60 (1-2) ◽  
pp. 1-25 ◽  
Author(s):  
Xin-You Meng ◽  
Hai-Feng Huo ◽  
Xiao-Bing Zhang
Keyword(s):  
Hopf Bifurcation ◽  
Stage Structure ◽  
Global Hopf Bifurcation ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

scholarly journals STABILITY AND HOPF BIFURCATION OF A MODIFIED DELAY PREDATOR-PREY MODEL WITH STAGE STRUCTURE

2018 ◽  
Vol 8 (2) ◽  
pp. 573-597
Author(s):  
Jing Li ◽  
◽  
Shaotao Zhu ◽  
Ruilan Tian ◽  
Wei Zhang ◽  
...  
Keyword(s):  
Hopf Bifurcation ◽  
Stage Structure ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

scholarly journals Hopf bifurcation and stability analysis of the Rosenzweig-MacArthur predator-prey model with stage-structure in prey

2020 ◽  
Vol 17 (4) ◽  
pp. 4080-4097 ◽  
Author(s):  
Lazarus Kalvein Beay ◽  
◽  
Agus Suryanto ◽  
Isnani Darti ◽  
Trisilowati ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Stage Structure ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Bifurcation And Stability

scholarly journals Stability and Global Hopf Bifurcation Analysis on a Ratio-Dependent Predator-Prey Model with Two Time Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-15
Author(s):  
Huitao Zhao ◽  
Yiping Lin ◽  
Yunxian Dai
Keyword(s):  
Hopf Bifurcation ◽  
Time Delays ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Positive Equilibrium ◽  
Global Hopf Bifurcation ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Ratio Dependent

A ratio-dependent predator-prey model with two time delays is studied. By means of an iteration technique, sufficient conditions are obtained for the global attractiveness of the positive equilibrium. By comparison arguments, the global stability of the semitrivial equilibrium is addressed. By using the theory of functional equation and Hopf bifurcation, the conditions on which positive equilibrium exists and the quality of Hopf bifurcation are given. Using a global Hopf bifurcation result of Wu (1998) for functional differential equations, the global existence of the periodic solutions is obtained. Finally, an example for numerical simulations is also included.

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