关于系统x=φ(y)-F(x),y=-g(x)的极限环之唯一性

On the Uniqueness of Limit Cycle of System =φ(y)-F(x),=-g(x)

对非线性系统 (1)用文献 [1]的思路和方法 ,给出了一个极限环存在的唯一性定理 ,去掉了文献 [1]定理 1的条件 1) ,使该定理的条件更容易验证 ;然后将该定理应用于以生化反应为背景的一类平面四次微分系统 ,得到了该系统有唯一单重稳定的极限环的充分条件 ;应用于文献 [3]的三次系统 ,所得结论与文献

In this paper,we give the uniqueness theorem of limit cycle to system =(y)-F(x),=-g(x) by using idea and method for paper,in which if the hypothesis 1) of the theorem 1 for is omitted;it is easier to prove the conditions of the theorem.Then we obtain some sufficient conditions of one simple stable limit cycle for a plane 4-degree system in biochemical reactions,the 3-degree system method that is applied to paper,it has the same evidence as paper.