Dynamical analysis of a harvested predator-prey model with ratio-dependent response function and prey refuge

2014 ◽  
Vol 8 ◽  
pp. 5027-5037 ◽  
Author(s):  
N. N. Ilmiyah ◽  
Trisilowati ◽  
A. R. Alghofari
Keyword(s):  
Response Function ◽  
Dynamical Analysis ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Ratio Dependent

Dynamical analysis of a fractional-order predator-prey model incorporating a prey refuge

2016 ◽  
Vol 54 (1-2) ◽  
pp. 435-449 ◽  
Author(s):  
Hong-Li Li ◽  
Long Zhang ◽  
Cheng Hu ◽  
Yao-Lin Jiang ◽  
Zhidong Teng
Keyword(s):  
Fractional Order ◽  
Dynamical Analysis ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

scholarly journals Stability Analysis of a Ratio-Dependent Predator-Prey Model Incorporating a Prey Refuge

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Lingshu Wang ◽  
Guanghui Feng
Keyword(s):  
Sufficient Conditions ◽  
Stage Structure ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Comparison Arguments ◽  
Ratio Dependent ◽  
Iteration Technique ◽  
Coexistence Equilibrium

A ratio-dependent predator-prey model incorporating a prey refuge with disease in the prey population is formulated and analyzed. The effects of time delay due to the gestation of the predator and stage structure for the predator on the dynamics of the system are concerned. By analyzing the corresponding characteristic equations, the local stability of a predator-extinction equilibrium and a coexistence equilibrium of the system is discussed, respectively. Further, it is proved that the system undergoes a Hopf bifurcation at the coexistence equilibrium, whenτ=τ0. By comparison arguments, sufficient conditions are obtained for the global stability of the predator-extinction equilibrium. By using an iteration technique, sufficient conditions are derived for the global attractivity of the coexistence equilibrium of the proposed system.

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