CANARDS AT FOLDED NODES

被引：39

作者：

Guckenheimer, John ^{[1
]}

Haiduc, Radu ^{[1
]}

机构：

[1] Cornell Univ, Ithaca, NY 14853 USA

来源：

MOSCOW MATHEMATICAL JOURNAL | 2005年 / 5卷 / 01期

基金：

美国国家科学基金会;

关键词：

Folded node; singularly perturbed system; slow-fast vector field;

D O I：

10.17323/1609-4514-2005-5-1-91-103

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Folded singularities occur generically in singularly perturbed systems of differential equations with two slow variables and one fast variable. The folded singularities can be saddles, nodes or foci. Canards are trajectories that flow from the stable sheet of the slow manifold of these systems to the unstable sheet of their slow manifold. Benoit has given a comprehensive description of the flow near a folded saddle, but the phase portraits near folded nodes have been only partially described. This paper examines these phase portraits, presenting a picture of the flows in the case of a model system with a folded node. We prove that the number of canard solutions in these systems is unbounded.

引用

页码：91 / 103

页数：13

共 11 条

[1]

Arnold V. I., 1986, ENCYCL MATH SCI, V5, P5

[2] Singular perturbation, tridimensional case :: canards on a pseudo-singular node point [J].