SHARP UPPERBOUNDS FOR THE NUMBER OF LARGE AMPLITUDE LIMIT CYCLES IN POLYNOMIAL LIENARD SYSTEMS

被引：3

作者：

Dumortier, Freddy ^{[1
]}

机构：

[1] Univ Hasselt, B-3590 Diepenbeek, Belgium

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2012年 / 32卷 / 05期

关键词：

Lienard equation; Limit cycle; Heteroclinic connection; Cyclicity; EQUATIONS;

D O I：

10.3934/dcds.2012.32.1465

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In [1] and [2] upperbounds have been given for the number of large amplitude limit cycles in polynomial Lienard systems of type (m, n) with m < 2n + 1, m and n odd. In the current paper we improve the upperbounds from [1] and [2] by one unity, obtaining sharp results. We therefore introduce the "method of cloning variables" that might be useful in other cyclicity problems.

引用

页码：1465 / 1479

页数：15

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