Degenerate Hopf bifurcations in discontinuous planar systems

被引：132

作者：

Coll, B ^{[1
]}

Gasull, A

Prohens, R

机构：

[1] Univ Illes Balears, Fac Ciencies, Dept Matemat & Informat, Palma de Mallorca 7071, Spain

[2] Univ Autonoma Barcelona, Dept Math, Barcelona 08193, Spain

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2001年 / 253卷 / 02期

关键词：

D O I：

10.1006/jmaa.2000.7188

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the stability of a singular point for planar discontinuous differential equations with a line of discontinuities. This is done. for the most generic cases. by computing some kind of Lyapunov constants. Our computations are based on the so called (R, theta, p, q)-generalized polar coordinates, introduced by Lyapunov, and they are essentially different from the ones used in the smooth case. These Lyapunov constants are also used to generate limit cycles for some concrete examples. (C) 2001 Academic Press.

引用

页码：671 / 690

页数：20

共 15 条

[1] NONAUTONOMOUS EQUATIONS RELATED TO POLYNOMIAL TWO-DIMENSIONAL SYSTEMS [J].

ALWASH, MAM ;

LLOYD, NG .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1987, 105 :129-152

[2]

Andronov A.A., 1973, Theory of bifurcations of dynamic systems on a plane

[3]

Andronov AA., 1996, THEORY OSCILLATORS

[4]

Bautin N., 1954, AM MATH SOC TRANSL, V100, P397

[5] THE NUMBER OF LIMIT-CYCLES OF CERTAIN POLYNOMIAL DIFFERENTIAL-EQUATIONS [J].

BLOWS, TR ;

LLOYD, NG .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1984, 98 :215-239

[6]

Broer H., 1991, STRUCTURES DYNAMICS

[7] Algebraic properties of the Liapunov and period constants [J].

Cima, A ;

Gasull, A ;

Manosa, V ;

Manosas, F .

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 1997, 27 (02) :471-501

[8] Differential equations defined by the sum of two quasi-homogeneous vector fields [J].

Coll, B ;

Gasull, A ;

Prohens, R .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1997, 49 (02) :212-231

[9] DEGENERATE HOPF-BIFURCATION FORMULAS AND HILBERTS 16TH PROBLEM [J].

FARR, WW ;

LI, CZ ;

LABOURIAU, IS ;

LANGFORD, WF .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1989, 20 (01) :13-30

[10]

Filippov A.F., 1988, MATH ITS APPL SOVIET, V18

← 1 2 →