一类生化反应系统的定性分析

Qualitative Analysis of a Class of Biochemical Reaction System

研究如下一类具米氏（Michalis）反应速度的化学反应模型dX/dt=A-BX-XY^2,dY/dt+BX+XY^2-υY/k+Y'其中A，B，v及k为正常数，应用微分方程定性理论，在一定条件下研究了上述系统极限环的存在性，不存在性及唯一性问题．

This paper is devoted to study the following chemical reaction model with Michalis reaction speed dX/dt=A-BX-XY^2,dY/dt=BX+XY^2-υY/k+Y'where A,B,v and k are all positive constants.By using qualitative theory of ordinary differential equations,the conditions of existence, nonexistence and uniqueness of limit cycle about the above system are obtained.