Hopf bifurcation analysis of a delayed diffusive predator–prey system with nonconstant death rate

2015 ◽  
Vol 81 ◽  
pp. 224-232 ◽  
Author(s):  
Ruizhi Yang
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Death Rate ◽  
Predator Prey ◽  
Prey System

scholarly journals Hopf Bifurcation Analysis of a Predator-Prey Biological Economic System with Nonselective Harvesting

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Biwen Li ◽  
Zhenwei Li ◽  
Boshan Chen ◽  
Gan Wang
Keyword(s):  
Hopf Bifurcation ◽  
Economic System ◽  
Bifurcation Analysis ◽  
Economic Perspective ◽  
Modified Model ◽  
Bifurcation Theorem ◽  
Predator Prey ◽  
Economic Profit ◽  
Prey System ◽  
Nonselective Harvesting

A modified predator-prey biological economic system with nonselective harvesting is investigated. An important mathematical feature of the system is that the economic profit on the predator-prey system is investigated from an economic perspective. By using the local parameterization method and Hopf bifurcation theorem, we analyze the Hopf bifurcation of the proposed system. In addition, the modified model enriches the database for the predator-prey biological economic system. Finally, numerical simulations illustrate the effectiveness of our results.

Hopf Bifurcation Analysis of a Predator Prey System Involving Switching

1996 ◽  
Vol 65 (3) ◽  
pp. 864-867 ◽  
Author(s):  
Q. J. A. Khan ◽  
B. S. Bhatt ◽  
R. P. Jaju
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Predator Prey ◽  
Prey System

THE EFFECT OF DIFFUSION FOR A PREDATOR–PREY SYSTEM WITH NONMONOTONIC FUNCTIONAL RESPONSE

2004 ◽  
Vol 14 (12) ◽  
pp. 4309-4316 ◽  
Author(s):  
ZHIHUA LIU ◽  
RONG YUAN
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Functional Response ◽  
Bifurcation Analysis ◽  
Predator Prey ◽  
Prey System ◽  
Nonmonotonic Functional Response

We consider the delayed predator–prey system with diffusion. The bifurcation analysis of the model shows that Hopf bifurcation can occur under some conditions and the system has a Bogdanov–Takens singularity for any time delay value.

scholarly journals Dynamics of a Predator-Prey System with a Mate-Finding Allee Effect

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Ruiwen Wu ◽  
Xiuxiang Liu
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Allee Effect ◽  
Blow Up ◽  
Mate Finding ◽  
Predator Prey ◽  
Stability Properties ◽  
Prey System ◽  
The Stability ◽  
High Possibility

We consider a ratio-dependent predator-prey system with a mate-finding Allee effect on prey. The stability properties of the equilibria and a complete bifurcation analysis, including the existence of a saddle-node, a Hopf bifurcation, and, a Bogdanov-Takens bifurcations, have been proved theoretically and numerically. The blow-up method has been applied to investigate the structure of a neighborhood of the origin. Our mathematical results show the mate-finding Allee effect can reduce the complexity of system behaviors by making the complicated equilibrium less complicated, and it can be a destabilizing force as well, which makes the system has a high possibility of being threatened with extinction in ecology.

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