Bifurcation of Limit Cycles for a Perturbed Piecewise Quadratic Differential Systems

被引：4
作者：
Ji, Gui Lin [1 ]
Liu, Chang Jian [1 ]
Li, Peng Heng [1 ]
机构：
[1] Sun Yat Sen Univ, Sch Math Zhuhai, Zhuhai 519082, Peoples R China
来源：
ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2022年 / 38卷 / 03期
关键词：
Piecewise system; limit cycle; Abelian integral; AVERAGING THEORY; NUMBER;
D O I：
10.1007/s10114-022-0513-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, the bifurcation of limit cycles for planar piecewise smooth systems is studied which is separated by a straight line. We give a new form of Abelian integrals for piecewise smooth systems which is simpler than before. In application, for piecewise quadratic system the existence of 10 limit cycles and 12 small-amplitude limit cycles is proved respectively.
引用
收藏
页码：591 / 611
页数：21
相关论文
共 30 条
  • [1] Piecewise linear differential systems with two real saddles
    Artes, Joan C.
    Llibre, Jaume
    Medrado, Joao C.
    Teixeira, Marco A.
    [J]. MATHEMATICS AND COMPUTERS IN SIMULATION, 2014, 95 : 13 - 22
  • [2] Banerjee S., 2001, NONLINEAR PHENOMENA
  • [3] Boulier F., 2014, COMPUTER MATH
  • [4] On the Equivalence of the Melnikov Functions Method and the Averaging Method
    Buica, Adriana
    [J]. QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2017, 16 (03) : 547 - 560
  • [5] Limit cycles in planar piecewise linear differential systems with nonregular separation line
    Cardin, Pedro Toniol
    Torregrosa, Joan
    [J]. PHYSICA D-NONLINEAR PHENOMENA, 2016, 337 : 67 - 82
  • [6] Limit cycles bifurcate from centers of discontinuous quadratic systems
    Chen, Xingwu
    Du, Zhengdong
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 59 (12) : 3836 - 3848
  • [7] Christopher C, 2005, TRENDS MATH, P23
  • [8] Coll B, 2005, DYNAM CONT DIS SER A, V12, P275
  • [9] New lower bound for the Hilbert number in piecewise quadratic differential systems
    da Cruz, Leonardo P. C.
    Novaes, Douglas D.
    Torregrosa, Joan
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2019, 266 (07) : 4170 - 4203
  • [10] Control of near-grazing dynamics in impact oscillators
    Dankowicz, H
    Jerrelind, J
    [J]. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2005, 461 (2063): : 3365 - 3380
123