Bifurcation of limit cycles from a heteroclinic loop with a cusp

被引：42

作者：

Sun, Xianbo ^{[1
]}

Han, Maoan ^{[1
]}

Yang, Junmin ^{[2
]}

机构：

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

[2] Hebei Normal Univ, Coll Math & Informat Sci, Shijiazhuang 050016, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2011年 / 74卷 / 09期

基金：

中国国家自然科学基金;

关键词：

Nilpotent cusp; Heteroclinic loop; Melnikov function; Limit cycle; Bifurcation; POLYNOMIAL VECTOR-FIELDS; SYSTEMS;

D O I：

10.1016/j.na.2011.01.013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we study the expansion of the first Melnikov function of a near-Hamiltonian system near a heteroclinic loop with a cusp and a saddle or two cusps, obtaining formulas to compute the first coefficients of the expansion. Then we use the results to study the problem of limit cycle bifurcation for two polynomial systems. (c) 2011 Elsevier Ltd. All rights reserved.

引用

页码：2948 / 2965

页数：18

共 8 条

[1]

[Anonymous], 2006, HDB DIFFERENTIAL EQU

[2] Bifurcations of limit cycles from quintic Hamiltonian systems with an eye-figure loop (II) [J].

Asheghi, Rasoul ;

Zangeneh, Hamid R. Z. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 69 (11) :4143-4162

[3]

HAN MA, 1994, SCI CHINA SER A, V37, P1325

[4] Limit Cycles Near Homoclinic and Heteroclinic Loops [J].

Han, Maoan ;

Yang, Junmin ;

Tarta, Alexandrina -Alina ;

Gao, Yang .

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2008, 20 (04) :923-944

[5] Hilbert's 16th problem and bifurcations of planar polynomial vector fields [J].

Li, JB .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2003, 13 (01) :47-106

[6] Limit cycles of a Z3-equivariant near-Hamiltonian system [J].

Ma, Hongyan ;

Han, Maoan .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (09) :3853-3871

[7]

Roussarie R., 1986, P CAMB PHILOS SOC, V95, P359

[8]

SCHLOMIUK D, 1993, NATO ADV SCI INST SE, V408, P429

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