生化反应中一类动力系统的定性分析

考虑生化反应中的一个动力系统dx/ dt=1 - xy　　 dy/ dt=(xy - y)利用微分方程的定性理论 ,研究了 (1 )之极限环的存在及不存在的条件 ,得到结果 :存在 α* >1 / 2 ,使当 1 / 2<α<α* 时 (1 )有唯一稳定的极限环 ;当 0 <α≤ 1 / 2时 ,(1 )没有极限环。

QUALITATIVE ANALYSIS OF A DYNAMICAL SYSTEM IN BIOCHEMISTRY REACTION

By using qualitative theory of differential equations, we studied the existence.nonexistence and uniqueness of limit cycle of a dynamical system in biochemistry reaction dx/dt = 1 - xy dy/dr = (xy - y)and obtained the following result: there exist a constant a' ＞1/2 such that the system bas no limit cycle for 0＜≤≤1/2 and it has an unique stable limit cycle for 1/2＜≤a*.