HOPF BIFURCATION OF LIENARD SYSTEMS BY PERTURBING A NILPOTENT CENTER

被引：3

作者：

Su, Jing ^{[1
]}

Yang, Junmin ^{[2
]}

Han, Maoan ^{[1
]}

机构：

[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

[2] Hebei Normal Univ, Coll Math & Informat Sci, Shijiazhuang 050024, Peoples R China

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2012年 / 22卷 / 08期

基金：

中国国家自然科学基金;

关键词：

Hopf bifurcation; Lienard system; nilpotent center; Melnikov function; NEAR-HAMILTONIAN SYSTEMS; LIMIT-CYCLES;

D O I：

10.1142/S0218127412502033

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

As we know, Lienard system is an important model of nonlinear oscillators, which has been widely studied. In this paper, we study the Hopf bifurcation of an analytic Lienard system by perturbing a nilpotent center. We develop an efficient method to compute the coefficients b(l) appearing in the expansion of the first order Melnikov function by finding a set of equivalent quantities B2l+1 which are able to calculate directly and can be used to study the number of small-amplitude limit cycles of the system. As an application, we investigate some polynomial Lienard systems, obtaining a lower bound of the maximal number of limit cycles near a nilpotent center.

引用

页数：7

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