On the Melnikov functions and limit cycles near a double homoclinic loop with a nilpotent saddle of order (m)over-cap

被引：4

作者：

Yang, Junmin ^{[1
,2
]}

Yu, Pei ^{[2
]}

Han, Maoan ^{[3
,4
]}

机构：

[1] Hebei Normal Univ, Sch Math Sci, Shijiazhuang 050024, Hebei, Peoples R China

[2] Western Univ, Dept Appl Math, London, ON N6A 5B7, Canada

[3] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China

[4] Shanghai Normal Univ, Math & Sci Coll, Shanghai 200234, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2021年 / 291卷

基金：

加拿大自然科学与工程研究理事会; 中国国家自然科学基金;

关键词：

Melnikov function; Limit cycle; Bifurcation; Lienard system; HAMILTONIAN-SYSTEMS; BIFURCATIONS; NUMBER; HOPF;

D O I：

10.1016/j.jde.2021.04.032

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a centrally symmetric near-Hamiltonian system, we develop a method for computing all the coefficients in the expansions of three Melnikov functions near a double homoclinic loop. Moreover, we give a new estimation on the lower bound of H(2 (n) over cap, 5) for 11 <= (n) over cap <= 23, where H(2 (n) over cap, 5) is the maximal number of limit cycles for a kind of Lienard system, (x) over dot = y, (y) over dot = -g(x) + epsilon f (x)y, with deg g(x) = 5 and deg f (x) = 2 (n) over cap. (C) 2021 Elsevier Inc. All rights reserved.

引用

页码：27 / 56

页数：30

共 15 条

[1] Limit cycle bifurcations near a double homoclinic loop with a nilpotent saddle of order m
Yang, Junmin
Yu, Pei
Han, Maoan
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Yang Junmin Han Maoan (Dept.of Math.
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HAN MAOAN BI PING Department of Mathematics
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[J]. DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2019, 2019
[10] THE NUMBER OF LIMIT CYCLES NEAR A DOUBLE HOMOCLINIC LOOP FOR A NEAR-HAMILTONIAN SYSTEM
Xu, Xiaoyu
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Han, Tong
[J]. JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2024, 14 (02): : 1111 - 1132

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