On the Liénard system with two isoclines

Mathematica Slovaca

Makoto Hayashi¹ 

关键词: Liénard system;    limit cycle;    heteroclinic orbit;    isocline;   

DOI  :  10.2478/s12175-009-0144-1

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

In this paper, the non-existence of limit cycles of a Liénard system ẋ = y−F(x), ẏ = −g(x) is discussed. By using the transformation y = z+ϕ(x) to the system, the new system has two special isoclines. We call the curves Vertical isocline or Horizontal isocline, respectively. It shall be shown that the existence of these isoclines play an important role in the non-existence of limit cycles of the system. The results are applied to many examples, and the known results are improved in certain cases.

【 授权许可】

Unknown