Limit cycles in a Lienard system with a cusp and a nilpotent saddle of order 7

被引：6

作者：

Asheghi, R. ^{[1
]}

Bakhshalizadeh, A. ^{[1
]}

机构：

[1] Isfahan Univ Technol, Dept Math Sci, Esfahan 8415683111, Iran

来源：

CHAOS SOLITONS & FRACTALS | 2015年 / 73卷

关键词：

NEAR-HAMILTONIAN SYSTEMS; DIFFERENTIAL-EQUATIONS; MELNIKOV FUNCTIONS; HOMOCLINIC LOOP; BIFURCATIONS; UNIQUENESS;

D O I：

10.1016/j.chaos.2015.01.009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we first give the topological classification of level curves for a special Lienard system. Then we study the number of limit cycles of some polynomial Lienard systems with a cuspidal loop surrounded by a loop that is connected (homoclinic) to a nilpotent saddle. We prove that H(5, 6) >= 9,H(6,6) >= 10 and H(7,6) >= 11, where H(m,n) is the maximal number of limit cycles in a Lienard system of type (m, n). (C) 2015 Elsevier Ltd. All rights reserved.

引用

页码：120 / 128

页数：9

共 25 条

[1]

[Anonymous], 1928, REV GENERALE LELECTR, DOI DOI 10.1016/J.JWEIA.2013.09.002

[2]

Blows TR, 1984, MATH P CAMB PHILOS S, V95, P59

[3] Small-amplitude limit cycle bifurcations for Lienard systems with quadratic or cubic damping or restoring forces [J].

Christopher, C ;

Lynch, S .

NONLINEARITY, 1999, 12 (04) :1099-1112

[4]

Coppel WA., 1989, Dynamics Reported, P61, DOI 10.1007/978-3-322-96657-5_3

[5] CUBIC LIENARD EQUATIONS WITH LINEAR DAMPING [J].

DUMORTIER, F ;

ROUSSEAU, C .

NONLINEARITY, 1990, 3 (04) :1015-1039

[6] On the uniqueness of limit cycles surrounding one or more singularities for Lienard equations [J].

Dumortier, F ;

Li, CZ .

NONLINEARITY, 1996, 9 (06) :1489-1500

[7] Quadratic Lienard equations with quadratic damping [J].

Dumortier, F ;

Li, CZ .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1997, 139 (01) :41-59

[8] Complete hyperelliptic integrals of the first kind and their non-oscillation [J].

Gavrilov, L ;

Iliev, ID .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 356 (03) :1185-1207

[9]

Han M., 1999, Ann. Differ. Equat, V15, P113

[10] Small-amplitude limit cycles of polynomial Li,nard systems [J].

Han MaoAn ;

Tian Yun ;

Yu Pei .

SCIENCE CHINA-MATHEMATICS, 2013, 56 (08) :1543-1556

← 1 2 3 →