BIFURCATION OF LIMIT CYCLES BY PERTURBING A PERIODIC ANNULUS WITH MULTIPLE CRITICAL POINTS

被引：6
|
作者：
Chang, Guifeng [1 ]
Han, Maoan [1 ]
机构：
[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2013年 / 23卷 / 08期
基金：
中国国家自然科学基金;
关键词：
Limit cycles; Abelian integral; bifurcation; polynomial system; GLOBAL BIFURCATION; SYSTEMS; FAMILY;
D O I：
10.1142/S0218127413501435
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we consider the planar system x. = -yF(x, y)+ epsilon P (x, y), y. = xF(x, y)+ eQ(x, y), where the set {F(x, y) = 0} consists of m nonzero points (a(i), b(i)) (i = 1,..., m) with multiple multiplicities, P(x, y) and Q(x, y) are arbitrary real polynomials. We study the number of limit cycles bifurcating from the periodic annulus surrounding the origin by using Abelian integrals and residue integration.
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页数：14
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