On the Li,nard system with two isoclines

被引：1

作者：

Hayashi, Makoto ^{[1
]}

机构：

[1] Nihon Univ, Dept Math, Coll Sci & Technol, Funabashi, Chiba 2748501, Japan

来源：

MATHEMATICA SLOVACA | 2009年 / 59卷 / 04期

关键词：

Lienard system; limit cycle; heteroclinic orbit; isocline; PERIODIC-SOLUTIONS; LIENARD SYSTEM; EQUATION;

D O I：

10.2478/s12175-009-0144-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, the non-existence of limit cycles of a Li,nard system a(0)< = y-F(x), a(0) = -g(x) is discussed. By using the transformation y = z+I center dot(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.

引用

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页码：505 / 515

页数：11

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