scholarly journals Oscillatory Turing Patterns in a Simple Reaction-Diffusion System

2007 ◽  
Vol 50 (91) ◽  
pp. 234 ◽  
Author(s):  
Ruey-Tarng Ruey-Tarng ◽  
Sy-Sang Sy-Sang ◽  
Philip K.
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Turing Patterns ◽  
Simple Reaction

Turing Patterns in a Reaction-Diffusion System

2006 ◽  
Vol 45 (4) ◽  
pp. 761-764 ◽  
Author(s):  
Wu Yan-Ning ◽  
Wang Ping-Jian ◽  
Hou Chun-Ju ◽  
Liu Chang-Song ◽  
Zhu Zhen-Gang
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Turing Patterns

Pattern formation arising from wave instability in a simple reaction‐diffusion system

1995 ◽  
Vol 103 (23) ◽  
pp. 10306-10314 ◽  
Author(s):  
Anatol M. Zhabotinsky ◽  
Milos Dolnik ◽  
Irving R. Epstein
Keyword(s):  
Pattern Formation ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Wave Instability ◽  
Simple Reaction

scholarly journals Hopf Bifurcation and Turing Instability Analysis for the Gierer–Meinhardt Model of the Depletion Type

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Lianchao Gu ◽  
Peiliang Gong ◽  
Hongqing Wang
Keyword(s):  
Hopf Bifurcation ◽  
Reaction Diffusion ◽  
Turing Instability ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Turing Patterns ◽  
System Parameters ◽  
System Equation ◽  
Representative Model ◽  
The Stability

The reaction diffusion system is one of the important models to describe the objective world. It is of great guiding importance for people to understand the real world by studying the Turing patterns of the reaction diffusion system changing with the system parameters. Therefore, in this paper, we study Gierer–Meinhardt model of the Depletion type which is a representative model in the reaction diffusion system. Firstly, we investigate the stability of the equilibrium and the Hopf bifurcation of the system. The result shows that equilibrium experiences a Hopf bifurcation in certain conditions and the Hopf bifurcation of this system is supercritical. Then, we analyze the system equation with the diffusion and study the impacts of diffusion coefficients on the stability of equilibrium and the limit cycle of system. Finally, we perform the numerical simulations for the obtained results which show that the Turing patterns are either spot or stripe patterns.

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