Cubic Lienard equations with quadratic damping (II)

被引：1

作者：

Wang Y.-Q. ^{[1
]}

Jing Z.-J. ^{[2
,3
]}

机构：

[1] Department of Applied Mathematics, College of Science, Nanjing Agricultural University

[2] Department of Mathematics, Hunan Normal University

[3] Academy of Mathematics and System Sciences, Chinese Academy of Sciences

来源：

Acta Mathematicae Applicatae Sinica | 2002年 / 18卷 / 1期

基金：

中国国家自然科学基金;

关键词：

Cubic lienard equations; Hopf bifurcation; Limit cycles; Stability;

D O I：

10.1007/s102550200008

中图分类号：

学科分类号：

摘要：

Applying Hopf bifurcation theory and qualitative theory, we show that the general cubic Lienard equations with quadratic damping have at most three limit cycles. This implies that the guess in which the system has at most two limit cycles is false. We give the sufficient conditions for the system has at most three limit cycles or two limit cycles. We present two examples with three limit cycles or two limit cycles by using numerical simulation. © Springer-Verlag 2002.

引用

页码：103 / 116

页数：13

共 24 条

[1]

Browder F., Mathematical Developments Arising from Hilbert Problems, (1976)

[2]

Copple W.A., Some Quadratic Systems with at Most One Limit Cycle. Dynamical Repoted, 2, pp. 61-68, (1988)

[3]

Dumortier F., Chengzhi Li., Quadratic Lienard equations with quadratic damping, J. of Differential Equations, 139, pp. 41-59, (1997)

[4]

Dumortier F., Cxhengzhi Li., On the uniqueness of limit cycles surrounding one or more singularities for Lienard equations, Nonlinearity, 9, pp. 1489-1500, (1996)

[5]

Dumortier F., Roussean C., Cubic Lienard equations with linear damping, Nonlinearity, 3, pp. 1015-1039, (1990)

[6]

Gao S., On the existence of at most 2 limit cycles surroudin multiple singular points for lienard equation, J. of Beijing Normal University, 28, 3, pp. 301-305, (1992)

[7]

Lefschetz L., Differential Equations. Geometric Theory, (1957)

[8]

Lienard A., Etude des Oscillations Entretenues, Revue Generale de I'Electricite, 23, pp. 901-912, (1928)

[9]

Lins A., De Melo W., Pugh C.C., On lienard equation, Lecture Notes in Mathematics, 597, pp. 335-357, (1977)

[10]

Llogd N.G., New Directions in Dynamical Systems, pp. 192-234, (1988)

← 1 2 3 →