Bifurcation analysis of a discrete-time ratio-dependent predator–prey model with Allee Effect

2016 ◽  
Vol 38 ◽  
pp. 288-302 ◽  
Author(s):  
Lifang Cheng ◽  
Hongjun Cao
Keyword(s):  
Discrete Time ◽  
Bifurcation Analysis ◽  
Allee Effect ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Time Ratio ◽  
Prey Model ◽  
Ratio Dependent

Chaos control in a discrete-time predator–prey model with weak Allee effect

2018 ◽  
Vol 11 (07) ◽  
pp. 1850089 ◽  
Author(s):  
Saheb Pal ◽  
Sourav Kumar Sasmal ◽  
Nikhil Pal
Keyword(s):  
Discrete Time ◽  
Allee Effect ◽  
Sufficient Conditions ◽  
Equilibrium Analysis ◽  
Flip Bifurcation ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
The Stability ◽  
The Impact

The stability of the predator–prey model subject to the Allee effect is an interesting topic in recent times. In this paper, we investigate the impact of weak Allee effect on the stability of a discrete-time predator–prey model with Holling type-IV functional response. The mathematical features of the proposed model are analyzed with the help of equilibrium analysis, stability analysis, and bifurcation theory. We provide sufficient conditions for the flip bifurcation by considering Allee parameter as the bifurcation parameter. We observe that the model becomes stable from chaotic dynamics as the Allee parameter increases. Further, we observe bi-stability behavior of the model between only prey existence equilibrium and the coexistence equilibrium. Our analytical findings are illustrated through numerical simulations.

scholarly journals Bifurcation analysis of modified Leslie-Gower predator-prey model with double Allee effect

2018 ◽  
Vol 9 (4) ◽  
pp. 1263-1277 ◽  
Author(s):  
Manoj Kumar Singh ◽  
B.S. Bhadauria ◽  
Brajesh Kumar Singh
Keyword(s):  
Bifurcation Analysis ◽  
Allee Effect ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model
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