Limit Cycles for a Discontinuous Quintic Polynomial Differential System

被引：0
作者：
Bo Huang
机构：
[1] Beihang University,LMIB
[2] New York University,School of Mathematics and Systems Science
来源：
Qualitative Theory of Dynamical Systems | 2019年 / 18卷
关键词：
Averaging method; Center; Discontinuous quintic system; Limit cycle; Period annulus; 34C05; 34C07;
D O I：
暂无
中图分类号：
学科分类号：
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
收藏
页码：769 / 792
页数：23
相关论文
共 54 条
[1]  
Buicǎ A(2004)Averaging methods for finding periodic orbits via Brouwer degree Bull. Sci. Math. 128 7-22
[2]  
Llibre J(2010)On the number of zeros of Abelian integrals Invent. Math. 181 227-289
[3]  
Binyamini G(2005)Bifurcation of limit cycles from two families of centers Discrete Contin. Dyn. Syst. 12 275-287
[4]  
Novikov D(2006)A unified proof on the weak Hilbert 16th problem for J. Differ. Equ. 221 309-342
[5]  
Yakovenko S(2017)On the number of limit cycles for a class of discontinuous quadratic differential systems J. Math. Anal. Appl. 449 314-342
[6]  
Coll B(2018)New lower bound for the Hilbert number in piecewise quadratic differential systems J. Differ. Equ. 7 1-486
[7]  
Gasull A(2015)On the number of limit cycles in discontinuous piecewise linear differential systems with two pieces separated by a straight line J. Math. Anal. Appl. 424 475-497
[8]  
Prohens R(2001)The infinitesimal 16th Hilbert problem in the quadratic case Invent. Math. 143 449-76
[9]  
Chen FD(2009)Quadratic perturbations of quadratic codimension-four centers J. Math. Anal. Appl. 357 69-535
[10]  
Li C(2009)Perturbations of quadratic center of genus one Discrete Contin. Dyn. Syst. 25 511-1750072-16
123456