Note on limit cycles for m-piecewise discontinuous polynomial Lienard differential equations

被引：15

作者：

Dong, Guangfeng ^{[1
]}

Liu, Changjian ^{[2
]}

机构：

[1] Jinan Univ, Dept Math, Guangzhou 510632, Guangdong, Peoples R China

[2] Soochow Univ, Sch Math, Suzhou 215006, Peoples R China

来源：

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2017年 / 68卷 / 04期

关键词：

Limit cycle; Piecewise differential system; Lienard differential system; Averaging method;

D O I：

10.1007/s00033-017-0844-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the limit cycles for m-piecewise discontinuous polynomial Lienard differential systems of degree n with m/2 straight lines passing through the origin whose slopes are tan(alpha + 2j pi/m) for j = 0, 1, ... , m/2 - 1, and prove that for any positive even number m, if sin(m alpha/2) not equal 0, then there always exists such a system possessing at least [1/2(n - m-2/2)] limit cycles. This result verifies a conjecture proposed by Llibre and Teixerira (Z Angew Math Phys 66:51-66, 2015).

引用

页数：8

共 7 条

[1]

DiBernardo M, 2008, APPL MATH SCI, V163, P1, DOI 10.1007/978-1-84628-708-4

[2] Qualitative bifurcation analysis of a non-smooth friction-oscillator model [J].

Kunze, M ;

Kupper, T .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 1997, 48 (01) :87-101

[3] Averaging theory at any order for computing limit cycles of discontinuous piecewise differential systems with many zones [J].

Llibre, Jaume ;

Novaes, Douglas D. ;

Rodrigues, Camila A. B. .

PHYSICA D-NONLINEAR PHENOMENA, 2017, 353 :1-10

[4] Averaging theory for discontinuous piecewise differential systems [J].

Llibre, Jaume ;

Mereu, Ana C. ;

Novaes, Douglas D. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 258 (11) :4007-4032

[5] Limit cycles for m-piecewise discontinuous polynomial Li,nard differential equations [J].

Llibre, Jaume ;

Teixeira, Marco Antonio .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2015, 66 (01) :51-66

[6]

Novaes D. D., 2014, PUBL MAT EXTRA, P395

[7]

TEIXEIRA M. A., 2009, ENCY COMPLEXITY SYST

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