物理化学学报 >> 1989, Vol. 5 >> Issue (02): 191-195.doi: 10.3866/PKU.WHXB19890212

研究论文 上一篇    下一篇

用Lyapunov指数确定Brusselator和Oregonator的分岔

刘君利; 盖锋; 韩德刚; 林秋竹; 高执棣   

  1. 北京大学化学系
  • 收稿日期:1987-09-15 修回日期:1988-01-25 发布日期:1989-04-15
  • 通讯作者: 高执棣

DETERMINING BIFURCATION OF BRUSSELATOR AND OREGONATOR BY LYAPUNOV EXPONENT

Liu Junli; Gai Feng; Han Degang; Lin Qiuzhu; Gao Zhidi   

  1. Chemistry Department Peking University
  • Received:1987-09-15 Revised:1988-01-25 Published:1989-04-15
  • Contact: Gao Zhidi

摘要: 本文计算了Brusselator及Oregonator的Lyapunov指数随系统控制参量的变化,依据Lyapunov指数的稳定性理论,确定出上述两模型都是通过Hopf分岔产生极限环的。在Brusselator分岔行为上,Lyapunov指数理论与线性稳定性分析所得的结论是一致的。对Oregonator所代表的化学背景作了分析,指出影响B-Z反应发生分岔的主要因素是Br~-的再生能力与速度。

Abstract:

The variation of Lyapunov exponent of Brusselator and Oregonator with controlling parameters of systems has been calculated. It is determined that the limitcycles of the two models are all produced by Hopf bifurcation according to the theory of stability of Lyapunov exponent.The conclusion of this calculation is the same as that of the analysis of linear stability for the behavior of Brusselator bifurcation. By analyzing the chemical background of Oregonator it is demonstrated that the major factors havingeffect on B-Z system bifurcation are the producing ability and producing rate of bromide ion. So all factors having effect on the producing ability and producing rate of bromide ion may affect the state of system. Therefore the effect of organic substrates, the catalyst of metal ion, pH and temperature ect. on B-Z reaction can be explaioned.