Effect of cross-diffusion on the stationary problem of a predator–prey system with a protection zone

2018 ◽  
Vol 76 (9) ◽  
pp. 2262-2271 ◽  
Author(s):  
Wenbin Yang
Keyword(s):  
Stationary Problem ◽  
Predator Prey ◽  
Protection Zone ◽  
Cross Diffusion ◽  
Prey System

Pattern formation in a diffusive predator–prey system with cross-diffusion effects

2020 ◽  
Vol 100 (4) ◽  
pp. 4045-4060
Author(s):  
Xiaoling Li ◽  
Guangping Hu ◽  
Shiping Lu
Keyword(s):  
Pattern Formation ◽  
Predator Prey ◽  
Cross Diffusion ◽  
Prey System ◽  
Diffusion Effects

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 Turing Patterns in a Predator-Prey System with Self-Diffusion

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Hongwei Yin ◽  
Xiaoyong Xiao ◽  
Xiaoqing Wen
Keyword(s):  
Spatial Patterns ◽  
Nonlinear Diffusion ◽  
Turing Instability ◽  
Turing Patterns ◽  
Predator Prey ◽  
Self Diffusion ◽  
Cross Diffusion ◽  
Prey System ◽  
Diffusion Parameters ◽  
Normal Diffusion

For a predator-prey system, cross-diffusion has been confirmed to emerge Turing patterns. However, in the real world, the tendency for prey and predators moving along the direction of lower density of their own species, called self-diffusion, should be considered. For this, we investigate Turing instability for a predator-prey system with nonlinear diffusion terms including the normal diffusion, cross-diffusion, and self-diffusion. A sufficient condition of Turing instability for this system is obtained by analyzing the linear stability of spatial homogeneous equilibrium state of this model. A series of numerical simulations reveal Turing parameter regions of the interaction of diffusion parameters. According to these regions, we further demonstrate dispersion relations and spatial patterns. Our results indicate that self-diffusion plays an important role in the spatial patterns.

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