scholarly journals Stability and bifurcation of a delayed diffusive predator-prey system with food-limited and nonlinear harvesting

2020 ◽  
Vol 17 (4) ◽  
pp. 3520-3552
Author(s):  
Guangxun Sun ◽  
◽  
Binxiang Dai
Keyword(s):  
Predator Prey ◽  
Prey System ◽  
Stability And Bifurcation ◽  
Nonlinear Harvesting

scholarly journals Bogdanov-Takens and Triple Zero Bifurcations of a Delayed Modified Leslie-Gower Predator Prey System

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Xia Liu ◽  
Jinling Wang
Keyword(s):  
Center Manifold ◽  
Normal Form Theory ◽  
Center Manifold Reduction ◽  
Predator Prey ◽  
Interior Equilibrium ◽  
Prey System ◽  
Form Theory ◽  
Nonlinear Harvesting ◽  
Existence Conditions ◽  
Manifold Reduction

A delayed modified Leslie-Gower predator prey system with nonlinear harvesting is considered. The existence conditions that an equilibrium is Bogdanov-Takens (BT) or triple zero singularity of the system are given. By using the center manifold reduction, the normal form theory, and the formulae developed by Xu and Huang, 2008 and Qiao et al., 2010, the normal forms and the versal unfoldings for this singularity are presented. The Hopf bifurcation of the system at another interior equilibrium is analyzed by taking delay (small or large) as bifurcation parameter.

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