On the Number of Limit Cycles Bifurcating from the Linear Center with an Algebraic Switching Curve

被引：5

作者：

Wang, Jiaxin ^{[1
]}

Zhao, Liqin ^{[1
]}

Zhou, Jinping ^{[1
]}

机构：

[1] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2022年 / 21卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Limit cycle; The first order Melnikov function; Switching curve; DIFFERENTIAL-SYSTEMS; MELNIKOV ANALYSIS; PIECEWISE;

D O I：

10.1007/s12346-022-00614-w

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper studies the perturbations of system (x)over dot = y, (y)over dot = -x under arbitrary polynomial perturbations with switching curve y = x(m), where m is a positive integer. By analysing the first order Melnikov function, we obtain the lower bound and upper bound of the maximum number of limit cycles bifurcating from the period annulus if the first order Melnikov function is not identically 0.

引用

页数：42

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