生化反应中一类动力系统的定性分析

摘要

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*.%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.