Integrability and limit cycles in cubic Kukles systems with a nilpotent singular point

被引：2

作者：

Li, Feng ^{[1
]}

Li, Shimin ^{[2
]}

机构：

[1] Linyi Univ, Linyi, Shandong, Peoples R China

[2] Guangdong Univ Finance & Econ, Guangzhou, Guangdong, Peoples R China

来源：

NONLINEAR DYNAMICS | 2019年 / 96卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Kukles system; Center-focus problem; Nilpotent singular point; Normal form; Integrability; CENTER-FOCUS PROBLEM; BIFURCATION;

D O I：

10.1007/s11071-019-04805-0

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

In this paper, integrability problem and bifurcation of limit cycles for cubic Kukles systems which are assumed to have a nilpotent origin are investigated. A complete classification is given on the integrability conditions and proven to have a total of 7 cases. Bifurcation of limit cycles is also discussed; six or seven limit cycles can be obtained by two different perturbation methods. Integrability problem and bifurcation of limit cycles for the cubic Kukles systems with a nilpotent origin have been completely solved.

引用

页码：553 / 563

页数：11

共 32 条

[1] Generating limit cycles from a nilpotent critical point via normal forms [J].