一类非线性自治系统极限环的存在性

On the Existence of Limit Cycles for a Class of Nonlinear Differential Autonomous System

本文通过构造内外境界线的方法得到以下系统ddtx=p(y),ddty=-f(x)q(y)-g(x)极限环的存在性定理。其中在构造内境界线时考察来了奇点的稳定性,并选用正向有界的轨线作为外境界线的一部分,然后再根据Poincare-Bendixson环域定理得到本文的结果。

This paper is devoted to studying the existence of limit cycles of the following nonlinear differential autonomous system dx/dt=p（y）,dy/dt=-f（x）q（y）-g（x） which is generalized from the famous van del Pol equation.After researching the stability of the origin and some orbit whose positive semiorbit is bounded, we construct the Poincar e＇-Bandixon torus, the conclusion improves the corresponding results of [4,7].