BIFURCATIONS OF MULTIPLE RELAXATION OSCILLATIONS IN POLYNOMIAL LIENARD EQUATIONS

被引：12

作者：

De Maesschalck, P. ^{[1
]}

Dumortier, F. ^{[1
]}

机构：

[1] Hasselt Univ, B-3590 Diepenbeek, Belgium

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2011年 / 139卷 / 06期

关键词：

Slow-fast system; singular perturbations; limit cycles; relaxation oscillation; polynomial Lienard equations; elementary catastrophy; CANARD CYCLES;

D O I：

10.1090/S0002-9939-2010-10610-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove the presence of limit cycles of given multiplicity, together with a complete unfolding, in families of (singularly perturbed) polynomial Lienard equations. The obtained limit cycles are relaxation oscillations. Both classical Lienard equations and generalized Lienard equations are treated.

引用

页码：2073 / 2085

页数：13

共 50 条

[1] Multiple bifurcations in a polynomial model of bursting oscillations
de Vries, G
[J]. JOURNAL OF NONLINEAR SCIENCE, 1998, 8 (03) : 281 - 316
[2] Multiple Bifurcations in a Polynomial Model of Bursting Oscillations
G. de Vries
[J]. Journal of Nonlinear Science, 1998, 8 : 281 - 316
[3] Multiple Bifurcations in a Polynomial Model of Bursting Oscillations
De, Vries, G.
[J]. Journal of Nonlinear Science, 8 (03): : 281 - 316
[4] Bifurcations of relaxation oscillations
Guckenheimer, J
[J]. NORMAL FORMS, BIFURCATIONS AND FINITENESS PROBLEMS IN DIFFERENTIAL EQUATIONS, 2004, 137 : 295 - 316
[5] Oscillations for Lienard type equations
Herrmann, Leopold
[J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2008, 90 (01): : 60 - 65
[6] HOMOCLINIC BIFURCATIONS FOR PERIODICALLY LIENARD FORCED EQUATIONS
BELHAQ, M
CLERC, RL
HARTMANN, C
[J]. JOURNAL DE MECANIQUE THEORIQUE ET APPLIQUEE, 1987, 6 (06): : 865 - 877
[7] Polynomial Lienard equations near infinity
Dumortier, F
Herssens, C
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1999, 153 (01) : 1 - 29
[8] Compactification and desingularization of spaces of polynomial Lienard equations
Dumortier, F
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 224 (02) : 296 - 313
[9] Several kinds of oscillations in forced Lienard equations
Blot, Joel
Boudjema, Souhila
Cieutat, Philippe
[J]. BOUNDARY VALUE PROBLEMS, 2013,
[10] Local bifurcations of limit cycles, Abel equations and Lienard systems
Françoise, JP
[J]. NORMAL FORMS, BIFURCATIONS AND FINITENESS PROBLEMS IN DIFFERENTIAL EQUATIONS, 2004, 137 : 187 - 209

← 1 2 3 4 5 →