Predator invasion in predator–prey model with prey-taxis in spatially heterogeneous environment

2022 ◽  
Vol 65 ◽  
pp. 103495
Author(s):  
Wonhyung Choi ◽  
Inkyung Ahn
Keyword(s):  
Heterogeneous Environment ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

scholarly journals The study of global stability of a diffusive Michaelis-Menten and tanner predator-prey model

Filomat ◽  
2019 ◽  
Vol 33 (17) ◽  
pp. 5651-5659
Author(s):  
Demou Luo
Keyword(s):  
General Type ◽  
Equilibrium Solution ◽  
Positive Equilibrium ◽  
Heterogeneous Environment ◽  
Smooth Bounded Domain ◽  
Flux Boundary Condition ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Random Diffusion

In this paper, we consider a parabolic predator-prey model of Michaelis-Menten and Tanner functional response with random diffusion: ut = d1?u + au-bu2- ?uv/?u + v', vt = d2?v + rv- ?v2/u with d1,d2,a,b,r,?,?,? > 0 under the no-flux boundary condition in a smooth bounded domain ? ? Rn (n = 1,2,3). By applying a new method, we establish much improved global asymptotic stability of the unique positive equilibrium solution than works in literature. We also show the result can be extended to more general type of systems with heterogeneous environment.

scholarly journals Effects of dispersal for a predator-prey model in a heterogeneous environment

2019 ◽  
Vol 18 (5) ◽  
pp. 2511-2528 ◽  
Author(s):  
Yaying Dong ◽  
◽  
Shanbing Li ◽  
Yanling Li ◽  
◽  
...  
Keyword(s):  
Heterogeneous Environment ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

Uniqueness and multiplicity of positive solutions for a diffusive predator–prey model in the heterogeneous environment

2020 ◽  
Vol 150 (6) ◽  
pp. 3321-3348
Author(s):  
Shanbing Li ◽  
Yaying Dong
Keyword(s):  
Positive Solutions ◽  
Steady State Solution ◽  
Asymptotically Stable ◽  
Heterogeneous Environment ◽  
Globally Asymptotically Stable ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
The Stability ◽  
Multiplicity Of Positive Solutions

AbstractThis is the second part of our study on the spatially heterogeneous predator–prey model where the interaction is governed by a Crowley–Martin type functional response. In part I, we have proved that when the predator competition is strong (i.e. k is large), the model has at most one positive steady-state solution for any $\mu \in \mathbb {R}$, moreover it is globally asymptotically stable for any $\mu >0$. This part is denoted to study the effect of saturation. Our result shows that the large saturation coefficient (i.e. large m) can not only lead to the uniqueness of positive solutions, but also lead to the multiplicity of positive solutions, moreover the stability of the corresponding positive solutions is also completely obtained. This work can be regarded as a supplement of Ref. [10].

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