中国物理B ›› 2006, Vol. 15 ›› Issue (3): 513-517.doi: 10.1088/1009-1963/15/3/011

• GENERAL • 上一篇    下一篇

Relation between the complex Ginzburg--Landau equation and reaction--diffusion system

邵昕, 任毅, 欧阳颀   

  1. Department of Physics, Peking University, Beijing 100871,China
  • 收稿日期:2005-09-14 修回日期:2005-09-14 出版日期:2006-03-20 发布日期:2006-03-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10274003) and the Department of Science and Technology of China.

Relation between the complex Ginzburg--Landau equation and reaction--diffusion system

Shao Xin (邵昕), Ren Yi (任毅), Ouyang Qi (欧阳颀)   

  1. Department of Physics, Peking University, Beijing 100871,China
  • Received:2005-09-14 Revised:2005-09-14 Online:2006-03-20 Published:2006-03-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10274003) and the Department of Science and Technology of China.

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摘要： 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.

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.

Key words: complex Ginzburg--Landau equation, reaction--diffusion system, chlorite-iodide-malonic acid

中图分类号:  (Numerical simulations of chaotic systems)

  • 05.45.Pq
05.65.+b (Self-organized systems)