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Chinese Physics, 2006, Vol. 15(3): 513-517    DOI: 10.1088/1009-1963/15/3/011
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Relation between the complex Ginzburg--Landau equation and reaction--diffusion system

Shao Xin (邵昕), Ren Yi (任毅), Ouyang Qi (欧阳颀)
Department of Physics, Peking University, Beijing 100871,China
Abstract  The complex Ginzburg--Landau equation (CGLE) has been used to describe the travelling wave behaviour in reaction--diffusion (RD) systems. We argue that this description is valid only when the RD system is close to the Hopf bifurcation, and is not valid when a RD system is away from the onset. To test this, we study spirals and anti-spirals in the chlorite-iodide-malonic acid (CIMA) reaction and the corresponding CGLE. Numerical simulations confirm that the CGLE can only be applied to the CIMA reaction when it is very near the Hopf onset.
Keywords:  complex Ginzburg--Landau equation      reaction--diffusion system      chlorite-iodide-malonic acid  
Received:  14 September 2005      Revised:  14 September 2005      Accepted manuscript online: 
PACS:  05.45.Pq (Numerical simulations of chaotic systems)  
  05.65.+b (Self-organized systems)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No 10274003) and the Department of Science and Technology of China.

Cite this article: 

Shao Xin (邵昕), Ren Yi (任毅), Ouyang Qi (欧阳颀) Relation between the complex Ginzburg--Landau equation and reaction--diffusion system 2006 Chinese Physics 15 513

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