scholarly journals Hopf bifurcation analysis in a predator–prey model with two time delays and stage structure for the prey

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Miao Peng ◽  
Zhengdi Zhang
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Time Delays ◽  
Stage Structure ◽  
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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