scholarly journals Positive steady states of a ratio-dependent predator-prey system with cross-diffusion

2019 ◽  
Vol 16 (6) ◽  
pp. 6753-6768
Author(s):  
Xiaoling Li ◽  
◽  
Guangping Hu ◽  
Xianpei Li ◽  
Zhaosheng Feng ◽  
...  
Keyword(s):  
Steady States ◽  
Predator Prey ◽  
Cross Diffusion ◽  
Prey System ◽  
Positive Steady States ◽  
Ratio Dependent

scholarly journals STATIONARY PATTERNS OF A RATIO-DEPENDENT PREDATOR-PREY SYSTEM WITH CROSS-DIFFUSION

2011 ◽  
Vol 16 (3) ◽  
pp. 461-474 ◽  
Author(s):  
Yu-Xia Wang ◽  
Wan-Tong Li ◽  
Hong-Bo Shi
Keyword(s):  
Boundary Condition ◽  
Bounded Domain ◽  
Steady States ◽  
Flux Boundary Condition ◽  
Predator Prey ◽  
Cross Diffusion ◽  
Prey System ◽  
Positive Steady States ◽  
Ratio Dependent ◽  
The Cross

This paper is concerned with a ratio-dependent predator-prey system with diffusion and cross-diffusion in a bounded domain with no flux boundary condition. We establish the existence and non-existence of non-constant positive steady states (patterns). In particular, we show that under certain hypotheses, the cross-diffusion can create stationary patterns even though the corresponding model without cross-diffusion fails.

scholarly journals Positive Steady States of a Strongly Coupled Predator-Prey System with Holling-(n+1) Functional Response

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Xiao-zhou Feng ◽  
Zhi-guo Wang
Keyword(s):  
Functional Response ◽  
Neumann Boundary ◽  
Steady States ◽  
Diffusion Term ◽  
Strongly Coupled ◽  
Predator Prey ◽  
Prey System ◽  
Homogeneous Neumann Boundary Condition ◽  
Constant Solution ◽  
Positive Steady States

This paper discusses a predator-prey system with Holling-(n+1) functional response and the fractional type nonlinear diffusion term in a bounded domain under homogeneous Neumann boundary condition. The existence and nonexistence results concerning nonconstant positive steady states of the system were obtained. In particular, we prove that the positive constant solution(u~,v~)is asymptotically stable when the parameterksatisfies some conditions.

TURING PATTERNS OF A PREDATOR–PREY MODEL WITH A MODIFIED LESLIE–GOWER TERM AND CROSS-DIFFUSIONS

2012 ◽  
Vol 05 (06) ◽  
pp. 1250060 ◽  
Author(s):  
GUANG-PING HU ◽  
XIAO-LING LI
Keyword(s):  
Turing Instability ◽  
Turing Patterns ◽  
Positive Equilibrium ◽  
Asymptotically Stable ◽  
Strongly Coupled ◽  
Predator Prey ◽  
Cross Diffusion ◽  
Predator Prey Model ◽  
Prey System ◽  
Positive Steady States

In this paper, a strongly coupled diffusive predator–prey system with a modified Leslie–Gower term is considered. We will show that under certain hypotheses, even though the unique positive equilibrium is asymptotically stable for the dynamics with diffusion, Turing instability can produce due to the presence of the cross-diffusion. In particular, we establish the existence of non-constant positive steady states of this system. The results indicate that cross-diffusion can create stationary patterns.

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