Hopf bifurcation analysis in a predator-prey model with predator-age structure and predator-prey reaction time delay

2021 ◽  
Vol 91 ◽  
pp. 530-548
Author(s):  
Xiangming Zhang ◽  
Zhihua Liu
Keyword(s):  
Hopf Bifurcation ◽  
Reaction Time ◽  
Time Delay ◽  
Bifurcation Analysis ◽  
Age Structure ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

Hopf Bifurcation of a Delayed Predator–Prey Model with Nonconstant Death Rate and Constant-Rate Prey Harvesting

2018 ◽  
Vol 28 (14) ◽  
pp. 1850179 ◽  
Author(s):  
Fengrong Zhang ◽  
Xinhong Zhang ◽  
Yan Li ◽  
Changpin Li
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Differential Equations ◽  
Positive Constant ◽  
Death Rate ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Constant Rate ◽  
The Stability

This paper is concerned with a delayed predator–prey model with nonconstant death rate and constant-rate prey harvesting. We mainly study the impact of the time delay on the stability of positive constant solution of delayed differential equations and positive constant equilibrium of delayed diffusive differential equations, respectively. By choosing time delay [Formula: see text] as a bifurcation parameter, we show that Hopf bifurcation can occur as the time delay passes some critical values. In addition, the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are determined by using the normal form theory and center manifold theorem. Finally, some numerical simulations are carried out to depict our theoretical results.

Hopf bifurcation for a predator–prey model with age structure

2019 ◽  
Vol 526 ◽  
pp. 120953
Author(s):  
Dongxue Yan ◽  
Hui Cao ◽  
Xiaxia Xu ◽  
Xiaoqin Wang
Keyword(s):  
Hopf Bifurcation ◽  
Age Structure ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model
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