摘要
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。
By using qualitative theory of differential equations, we studied the existence, nonexistence and uniqueness of limit cycle of a dynamical system in biochemistry reactiondx/dt=1-xy dy/dt=(xy-y)and obtained the following result: there exist a constant α *>1/2 such that the system has no limit cycle for 0<≤1/2 and it has an unique stable limit cycle for 1/2<≤α *.
出处
《数学杂志》
CSCD
北大核心
2001年第3期281-284,共4页
Journal of Mathematics
