Turing pattern formation in a three species model with generalist predator and cross-diffusion

2013 ◽  
Vol 85 ◽  
pp. 214-232 ◽  
Author(s):  
Yunfei Lv ◽  
Rong Yuan ◽  
Yongzhen Pei
Keyword(s):  
Pattern Formation ◽  
Generalist Predator ◽  
Turing Pattern ◽  
Cross Diffusion

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

Turing Pattern Formation from the Cooperation of Competition and Cross-Diffusion

2014 ◽  
Vol 24 (03) ◽  
pp. 1450038 ◽  
Author(s):  
Xiyan Yang ◽  
Hongwei Yin ◽  
Tianshou Zhou
Keyword(s):  
Pattern Formation ◽  
Negative Feedback ◽  
Reaction Diffusion ◽  
Feedback Loops ◽  
Turing Patterns ◽  
Turing Pattern ◽  
Cross Diffusion ◽  
Interacting Species ◽  
Negative Feedback Loops ◽  
Positive And Negative Feedback

This paper investigates the pattern formation in a reaction–diffusion (R-D) system where two interacting species form coupled positive and negative feedback loops. It is found that the cooperation of competition and cross-diffusion can lead to the Turing pattern formation for which an adequate set of conditions are analytically derived. Such a mechanism of generating Turing patterns is different from the case that self-diffusion is sufficient to generate Turing patterns in a paradigm model (proverbially called as the Turing model) where two interacting species constitute a single negative feedback loop. Therefore, this work not only provides another model paradigm for studying the pattern formation but also would be helpful for understanding the formation of, for example, diversiform skin patterns in the mammalian world where coupled positive and negative feedback loops are ubiquitous.

TURING PATTERN FORMATION IN A TWO-SPECIES NEGATIVE FEEDBACK SYSTEM WITH CROSS-DIFFUSION

2013 ◽  
Vol 23 (09) ◽  
pp. 1350162 ◽  
Author(s):  
XIYAN YANG ◽  
ZHANJIANG YUAN ◽  
TIANSHOU ZHOU
Keyword(s):  
Pattern Formation ◽  
Negative Feedback ◽  
Sufficient Conditions ◽  
Feedback System ◽  
Turing Instability ◽  
Natural World ◽  
Mutual Diffusion ◽  
Turing Pattern ◽  
Reaction Diffusion Systems ◽  
Cross Diffusion

Pattern formation is a ubiquitous phenomenon in the natural world. Previous studies showed that for an activator–inhibitor system without cross-diffusion, spatial patterns can be formed only when the diffusion of the inhibitor is significantly faster than that of the activator. However, cross-diffusion exists extensively in real systems, especially in biological systems. Here, we study a prototypic two-species negative feedback system with cross-diffusion. By performing stability analysis of equilibrium state, we find sufficient conditions for Turing instability. Both analytical and numerical results demonstrate that mutual diffusions of the two species can lead to the Turing pattern formation regardless of differences in self-diffusion coefficients. However, in the absence of the mutual diffusion or even if there is the cross-diffusion of only one species, the system cannot exhibit Turing patterns. Our results reveal the mechanism of Turing pattern formation in a class of reaction–diffusion systems, where mutual diffusion between species plays a key role.

Turing Pattern Formation by the CIMA Reaction in a Chemical System Consisting of Quaternary Alkyl Ammonium Cationic Groups

2011 ◽  
Vol 115 (14) ◽  
pp. 3959-3963 ◽  
Author(s):  
Kouichi Asakura ◽  
Ryo Konishi ◽  
Tomomi Nakatani ◽  
Takaya Nakano ◽  
Masazumi Kamata
Keyword(s):  
Pattern Formation ◽  
Chemical System ◽  
Turing Pattern ◽  
Alkyl Ammonium ◽  
Cima Reaction
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