scholarly journals Stability and Hopf Bifurcation Analysis in a Delayed Gause-type Predator-prey Models

2018 ◽  
Author(s):  
Shuang Guo ◽  
Xing Qiao ◽  
Dongxia Zhao ◽  
Lianguang Jia ◽  
Xiuyan Jiang
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Predator Prey ◽  
Predator Prey Models

Hopf bifurcation analysis applied to predator-prey modeling

1992 ◽  
Vol 8 (2) ◽  
pp. 179-186 ◽  
Author(s):  
Peter Gross ◽  
Jeppe Sturis
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Predator Prey

scholarly journals Hopf Bifurcation Analysis on General Gause-Type Predator-Prey Models with Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Shuang Guo ◽  
Weihua Jiang
Keyword(s):  
Hopf Bifurcation ◽  
Center Manifold ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Center Manifold Theorem ◽  
Predator Prey Model ◽  
Normal Form Method ◽  
Predator Prey Models ◽  
The Stability

A class of three-dimensional Gause-type predator-prey model with delay is considered. Firstly, a group of sufficient conditions for the existence of Hopf bifurcation is obtained via employing the polynomial theorem by analyzing the distribution of the roots of the associated characteristic equation. Secondly, the direction of the Hopf bifurcation and the stability of the bifurcated periodic solutions are determined by applying the normal form method and the center manifold theorem. Finally, some numerical simulations are carried out to illustrate the obtained results.

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