物理化学学报 >> 1998, Vol. 14 >> Issue (10): 913-918.doi: 10.3866/PKU.WHXB19981010

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低浓度三分子双曲型反应-扩散方程的非线性理论

龚玉斌   

  1. 烟台师范学院物理系，山东 264025
  • 收稿日期:1997-12-28 修回日期:1998-04-07 发布日期:1998-10-15
  • 通讯作者:

Nonlinear Theory of the Hyperbolic Reaction-Diffusion Equations for the Low-Concentration Brusselator-Wave Equations

Gong Yu-Bin   

  1. Cepartment of Physics,Yantai Teachers University,Shandong 264025
  • Received:1997-12-28 Revised:1998-04-07 Published:1998-10-15
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摘要：

建立了低浓度三分子模型双曲型反应-扩散的波动方程，研究了定态的稳定性，重点研究了Turing不稳定问题，指出双曲型方程的Turing不稳定不受扩散系数不相等（Dx≠Dy）这一条件的约束，进而对方程作近似的分支分析，讨论了出现极限环的条件，最后对极限环和定态不稳定作了数值研究．

关键词: 三分子模型, 双曲型反应-扩散方程, Turing不稳定, 分支分析

Abstract:

The wave equations of the hyperbolic reaction-diffusion equations for the low-concentration Brusselator are developed, and the stability of steady state, especially Turing instability, is studied. The results show that the Turing instability in hyperbolic equations is not confined by the condition that coefficients are not equal(Dx≠Dy). Bifurcation analyses are carried out and the limit cycle is discussed. The numerical studies are also made.

Key words: Brussellator, Hyperbolic(Parabolic) reaction-diffusion equation, Turing instability, Bifureation analysis