Effects of Protection Zone and Nonlinear Growth on a Predator-Prey Model

2021 ◽  
Vol 176 (1) ◽  
Author(s):  
Yu-Xia Wang
Keyword(s):  
Predator Prey ◽  
Protection Zone ◽  
Nonlinear Growth ◽  
Predator Prey Model ◽  
Prey Model

scholarly journals Effect of a protection zone in the diffusive Leslie predator–prey model

2009 ◽  
Vol 246 (10) ◽  
pp. 3932-3956 ◽  
Author(s):  
Yihong Du ◽  
Rui Peng ◽  
Mingxin Wang
Keyword(s):  
Predator Prey ◽  
Protection Zone ◽  
Predator Prey Model ◽  
Prey Model

scholarly journals Effect of the protection zone in a diffusive ratio-dependent predator–prey model with fear and Allee effect

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Huan Wang ◽  
Hui Xing
Keyword(s):  
Mortality Rate ◽  
Allee Effect ◽  
Principal Eigenvalue ◽  
Neumann Boundary ◽  
Laplacian Operator ◽  
Predator Prey ◽  
Protection Zone ◽  
Predator Prey Model ◽  
Prey Model ◽  
Prior Estimate

AbstractIn this paper, we study the influence of a protection zone for the prey on a diffusive predator–prey model with fear factor and Allee effect. The prior estimate, global existence, nonexistence of nonconstant positive solutions and bifurcation from semitrivial solutions are well discussed. We show the existence of a critical patch value $\lambda ^{D}_{1}(\Omega _{0})$ λ 1 D ( Ω 0 ) of the protection zone, described by the principal eigenvalue of the Laplacian operator over $\Omega _{0}$ Ω 0 with Neumann boundary conditions. When the mortality rate of the predator $\mu \geq d_{2}\lambda ^{D}_{1}(\Omega _{0})$ μ ≥ d 2 λ 1 D ( Ω 0 ) , we show that the semitrivial solutions $(1,0)$ ( 1 , 0 ) and $(\theta,0)$ ( θ , 0 ) are unstable and there is no bifurcation occurring along respective semitrivial branches.

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