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

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