摘要
对一类具有二重饱和反应速度的生化反应动力系统进行研究,讨论了系统平衡点的稳定性态,对系统的极限环及Hopf分支现象进行分析.应用微分方程定性理论,研究该系统极限环存在唯一性的充分条件.引入适当的变换,将系统化简为规范形,同时利用动力系统中的规范形理论,研究该系统的Hopf分支.指出系统的平衡点为一阶稳定细焦点,当正平衡点不稳定时,一定存在唯一稳定极限环.最后,将系统与具有米氏饱和反应速度的生化反应动力系统的定性性质进行了比较.
A class of multimolecules saturated reaction model was studied and the stability of equilibrium was discussed. The limit cycle and the Hopf bifurcation behavior of the system were studied. The conditions of existence and uniqueness of limit cycles were obtained by using the qualitative theory of ordinary differential equations. The Hopf bifurcation behavior of the dynamic system was exploited by using the method of normal form theory and other approaches. It shows that the first order weak focus is stable. When the positive singular point is unstable,the system has unique stable limit cycle in the neighborhood of this critical point. At last we compared qualitative property of different systems with saturated reaction speed.
出处
《天津科技大学学报》
CAS
2009年第6期74-78,共5页
Journal of Tianjin University of Science & Technology
基金
国家自然科学基金资助项目(10872141)
天津科技大学科学研究基金资助项目(20070210)
关键词
饱和反应
极限环
HOPF分支
saturated reaction
limit cycle
Hopf bifurcation
