Bifurcation theory of limit cycles by higher order Melnikov functions and applications

被引：4

作者：

Liu, Shanshan ^{[1
]}

Han, Maoan ^{[1
]}

机构：

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

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2024年 / 403卷

基金：

国家重点研发计划;

关键词：

Higher order Melnikov function; Hopf bifurcation; Homoclinic bifurcation; Limit cycle; HAMILTONIAN-SYSTEMS; PERIODIC-SOLUTIONS; NUMBER; ORBITS; HOPF;

D O I：

10.1016/j.jde.2024.04.036

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study Poincar & eacute;, Hopf and homoclinic bifurcations of limit cycles for planar nearHamiltonian systems. Our main results establish Hopf and homoclinic bifurcation theories by higher order Melnikov functions, obtaining conditions on upper bounds and lower bounds of the maximum number of limit cycles. As an application, we concern a cubic near -Hamiltonian system, and study Hopf and homoclinic bifurcations in detail, finding more limit cycles than [26]. (c) 2024 Elsevier Inc. All rights reserved.

引用

页码：29 / 66

页数：38

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