scholarly journals Turing pattern formation in a predator–prey system with cross diffusion

2014 ◽  
Vol 38 (21-22) ◽  
pp. 5022-5032 ◽  
Author(s):  
Zhi Ling ◽  
Lai Zhang ◽  
Zhigui Lin
Keyword(s):  
Pattern Formation ◽  
Turing Pattern ◽  
Predator Prey ◽  
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

Pattern formation induced by cross-diffusion in a predator–prey system

2008 ◽  
Vol 17 (11) ◽  
pp. 3936-3941 ◽  
Author(s):  
Sun Gui-Quan ◽  
Jin Zhen ◽  
Liu Quan-Xing ◽  
Li Li
Keyword(s):  
Pattern Formation ◽  
Predator Prey ◽  
Cross Diffusion ◽  
Prey System

Pattern formation of a spatial predator–prey system

2012 ◽  
Vol 218 (22) ◽  
pp. 11151-11162 ◽  
Author(s):  
Gui-Quan Sun ◽  
Juan Zhang ◽  
Li-Peng Song ◽  
Zhen Jin ◽  
Bai-Lian Li
Keyword(s):  
Pattern Formation ◽  
Predator Prey ◽  
Prey System

scholarly journals Pattern Formation in Predator-Prey Model with Delay and Cross Diffusion

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Xinze Lian ◽  
Shuling Yan ◽  
Hailing Wang
Keyword(s):  
Time Delay ◽  
Pattern Formation ◽  
Turing Instability ◽  
Predator Prey ◽  
Cross Diffusion ◽  
Predator Prey Model ◽  
Prey Model ◽  
Diffusion Controlled ◽  
The Stability ◽  
Self Replication

We consider the effect of time delay and cross diffusion on the dynamics of a modified Leslie-Gower predator-prey model incorporating a prey refuge. Based on the stability analysis, we demonstrate that delayed feedback may generate Hopf and Turing instability under some conditions, resulting in spatial patterns. One of the most interesting findings is that the model exhibits complex pattern replication: the model dynamics exhibits a delay and diffusion controlled formation growth not only to spots, stripes, and holes, but also to spiral pattern self-replication. The results indicate that time delay and cross diffusion play important roles in pattern formation.

Sign in / Sign up

Export Citation Format

Share Document