General study on limit cycle bifurcation near a double homoclinic loop

被引：5

作者：

Han, Maoan ^{[1
]}

Yang, Junmin ^{[2
]}

Li, Jibin ^{[1
]}

机构：

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

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

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2023年 / 347卷

基金：

中国国家自然科学基金; 国家重点研发计划;

关键词：

Keywords limit cycle; Bifurcation; Melnikov function; HOPF;

D O I：

10.1016/j.jde.2022.11.031

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the bifurcation problem of limit cycles near a general double homoclinic loop. We establish a general theory to obtain a lower bound of the maximal number of limit cycles near the double homoclinic loop. As an application, we prove that a near-Hamiltonian system of the form x = n y(y2 - 1) + epsilon sigma i=0 that we can find so far for the system. (c) 2022 Elsevier Inc. All rights reserved. aix2i+1, y = -x has at least [52n] limit cycles for 1 < n < 56. This number is maximal

引用

页码：1 / 23

页数：23

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