关于系统x′=ψ(y)-F(x),y′=-g(x)的极限环

On Limit Cycles of Systemx′=φ(y)-F(x) y′=-g(x)

讨论了非线性系统（１）ｘ′＝φ（ｙ）－Ｆ（ｘ），ｙ′＝－ｇ（ｘ）应用菲里波夫变换方法，通过微分不等式，讨论了系统（１）积分曲线的走向，证明了在一定条件下，一个闭轨线不存在定理；应用反证法，通过比较一函数全微分在闭轨线上的积分，得到了在一定条件下，系统（１）的一个极限环的唯一性定理。

In this paper, we analyse the nonlinear system:(1)x′=(y)-F(x) y′=-g(x).We discuss the trend of integral curve about system (1) according to the change of ФИЛИЛЛОБ and differential inequality.We obtain a limit cycle nonexistence theorem under certain conditions. We compare the integral of a functions complete differential expression along limit cycle and reduction to absurdity and obtain a limit cycle uniqueness theorem of system (1) under certain conditions.