Limit Cycle Bifurcations in Perturbations of a Reversible Quadratic System with a Non-rational First Integral

被引：1

作者：

Xiong, Yanqin ^{[1
]}

Cheng, Rong ^{[1
]}

Li, Na ^{[2
]}

机构：

[1] Nanjing Univ Informat Sci & Technol, Sch Math & Stat, Nanjing 210044, Peoples R China

[2] Shanghai Univ Engn Sci, Sch Math Phys & Stat, Shanghai 201620, Peoples R China

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2020年 / 19卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Hopf cyclicity; Limit cycle; Melnikov function; Piecewise quadratic polynomial system; HAMILTONIAN-SYSTEMS; HILBERT NUMBER; CENTERS; HOPF;

D O I：

10.1007/s12346-020-00434-w

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper investigates the Hopf cyclicity of a piecewise smooth quadratic polynomial system by Melnikov function method, whose unperturbed system is a concrete reversible quadratic system with a center at the origin and with a non-rational first integral. By comparing the obtained result for the piecewise case with the result for the smooth case, it shows that the piecewise system can have at least four more limit cycles around the origin than the smooth one.

引用

页数：29

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