Stability and Hopf bifurcation analysis on a predator–prey model with discrete and distributed delays

2009 ◽  
Vol 10 (2) ◽  
pp. 1160-1172 ◽  
Author(s):  
Zhan-Ping Ma ◽  
Hai-Feng Huo ◽  
Chun-Ying Liu
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Distributed Delays ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

Stability and Hopf bifurcation analysis of a diffusive predator–prey model with Smith growth

2015 ◽  
Vol 08 (01) ◽  
pp. 1550013 ◽  
Author(s):  
M. Sivakumar ◽  
M. Sambath ◽  
K. Balachandran
Keyword(s):  
Boundary Condition ◽  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Neumann Boundary Condition ◽  
Local Stability ◽  
Neumann Boundary ◽  
Turing Instability ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

In this paper, we consider a diffusive Holling–Tanner predator–prey model with Smith growth subject to Neumann boundary condition. We analyze the local stability, existence of a Hopf bifurcation at the co-existence of the equilibrium and stability of bifurcating periodic solutions of the system in the absence of diffusion. Furthermore the Turing instability and Hopf bifurcation analysis of the system with diffusion are studied. Finally numerical simulations are given to demonstrate the effectiveness of the theoretical analysis.

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