Heteroclinic bifurcation of limit cycles in perturbed cubic Hamiltonian systems by higher-order analysis

被引：4

作者：

Geng, Wei ^{[1
]}

Han, Maoan ^{[2
]}

Tian, Yun ^{[1
]}

Ke, Ai ^{[2
]}

机构：

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

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

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2023年 / 357卷

基金：

中国国家自然科学基金;

关键词：

Heteroclinic bifurcation; Limit cycles; Higher-order Melnikov functions; MELNIKOV FUNCTIONS; PERTURBATIONS; LOOP; SADDLE; NUMBER; MAP;

D O I：

10.1016/j.jde.2023.02.027

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study heteroclinic bifurcation of limit cycles in a planar cubic near-Hamiltonian system by higher-order Melnikov functions. We compute the asymptotic expansion of the third-order Melnikov function near the heteroclinic loop Ls and prove that this system can have five limit cycles around Ls with proper perturbations.(c) 2023 Elsevier Inc. All rights reserved.

引用

页码：412 / 435

页数：24

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