Lienard方程的无穷远奇点与极限环

Critical Pointsot Infinity and Limit Cycle of Lienard Equation

本文利用文[1]中关于Lienard方程在无穷远奇点的特性和[3]中Hopf分枝定理,研究了Lienard方程+f(x)+g(x)=0极限环的存在性,这里,f(x),g(x)为多项式,给出了直接利用多项式系数就可以判断某些Lienard方程存在极限环的条件.并举例说明一些早期结果不能用于判断其极限环的存在性.

In this paper, we discuss the Lienard equation x = y-F(x) , y=-g(x) ( where f ( x ) (g(x)are polynomials ) on the basis of paper [1] , and obtain the existence of limit cycles for the Lienard equation by the coefficients of the polynomials as well as by the degree of polynomial.