物理化学学报 >> 1986, Vol. 2 >> Issue (02): 160-165.doi: 10.3866/PKU.WHXB19860210

研究论文 上一篇    下一篇

从多重定态经复杂奇点向极限环型化学振荡的跃迁

高森泉; 李如生   

  1. 清华大学化学与化学工程系
  • 收稿日期:1985-05-10 修回日期:1985-10-28 发布日期:1986-04-15

TRANSITION FROM MULTIPLE STEADY STATES TO CHEMICAL OSCILLATION THROUGH A COMPLICATED SINGULAR POINT

Gao Senquan; Li Rusheng   

  1. Department of Chemistry and Chemical Engineering, Tsinghua University, Beijing
  • Received:1985-05-10 Revised:1985-10-28 Published:1986-04-15

摘要: 在文Ⅰ~[1]的相平面分析的基础上, 利用线性稳定性分析和数值模拟的方法进一步分析了Schlögl模型在CSTR中的行为, 发现在适当条件下可以发生从定态向振荡态的不连续的突然跃迁现象。认为这种突然跃迁现象是通过鞍点-结点型复杂奇点的形成和消失而实现的。分析了这种鞍点-结点型跃迁与亚临界Hopf分支现象的差别, 并讨论了这种跃迁现象和实验上发现的某些突变型化学振荡现象之间的联系。

Abstract: Based on the results of phase plane analysis in paper I and using the technique of linear stability analysis and numerical simulation, the dynamic be- haviour of Schlögl model in CSTR is further analysed. It is shown that, with in- creasing the input concentration x° of species X but fixing the values of other parameters, the system may undergo the bifurcation from one steady state to three steady states and in turn to one steady state again, shown as in Fig.2.
Linear stability analysis shows that only one of the three branches of steady states for AFrom the point of view of bifurcation theory, above discontinuous transiton belongs the saddle-node transition, that is, the saddle point and node approach each other, merge into one compliated multiple singular point, and finally disappear and a limit cycle apears. This result would be helpful for explaination of some abrupt transition phenomena between steady state and oscillatory stte observed in some physical-chemical systems, such as B-Z reaction system.