Limit Cycles for a Discontinuous Quintic Polynomial Differential System

被引：5

作者：

Huang, Bo ^{[1
,2
]}

机构：

[1] Beihang Univ, LMIB Sch Math & Syst Sci, Beijing 100191, Peoples R China

[2] NYU, Courant Inst Math Sci, New York, NY 10012 USA

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2019年 / 18卷 / 03期

关键词：

Averaging method; Center; Discontinuous quintic system; Limit cycle; Period annulus; 34C05; 34C07; AVERAGING THEORY; 16TH PROBLEM; NUMBER; PERTURBATIONS; BIFURCATIONS;

D O I：

10.1007/s12346-018-00312-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we study the maximum number of limit cycles for a discontinuous quintic differential system. Using the first-order averaging method, we explain how limit cycles can bifurcate from the period annulus around the center of the considered system when it is perturbed inside a class of discontinuous quintic polynomial differential systems. Our results show that the lower bound and the upper bound of the number of limit cycles, 8 and 10 respectively, that can bifurcate from the period annulus around the center.

引用

页码：769 / 792

页数：24

共 25 条

[1]

Binyamini G, 2010, INVENT MATH, V181, P227, DOI 10.1007/s00222-010-0244-0

[2] Averaging methods for finding periodic orbits via Brouwer degree [J].