Limit cycle bifurcations near a double 2-polycycle on the cylinder

被引：3

作者：

Cai, Meilan ^{[1
]}

Han, Maoan ^{[2
]}

机构：

[1] Linyi Univ, Sch Math & Stat, Linyi 276005, Shandong, Peoples R China

[2] Zhejiang Normal Univ, Sch Math Sci, Jinhua 321004, Zhejiang, Peoples R China

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2024年 / 130卷

基金：

中国国家自然科学基金; 国家重点研发计划;

关键词：

Alien limit cycle; Bifurcation; Cylinder system; Stability; HOMOCLINIC LOOPS; SYSTEMS; QUANTITIES; STABILITY;

D O I：

10.1016/j.cnsns.2023.107737

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the bifurcation problem of limit cycles near a double 2-polycycle for cylinder near-Hamiltonian system. We first study the stability of a general homoclinic loop type II on the cylinder, and then obtain certain results on the number and distribution of limit cycles for the cylinder near-Hamiltonian system near the double 2-polycycle by using the Melnikov function method and the method of stability-changing of a homoclinic loop type I or II. Furthermore, we provide a way to find alien limit cycles for cylinder near Hamiltonian system. As applications, we obtain the number of limit cycles of a class of cylinder near-Hamiltonian systems.

引用

页数：29

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