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：
国家重点研发计划; 中国国家自然科学基金;
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
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页码：1 / 23
页数：23
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