Analysis of a slow-fast system near a cusp singularity

被引：9

作者：

Jardon-Kojakhmetov, H. ^{[1
]}

Broer, Henk W. ^{[1
]}

Roussarie, R. ^{[2
]}

机构：

[1] Univ Groningen, Johann Bernoulli Inst Math & Comp Sci, POB 407, NL-9700 AK Groningen, Netherlands

[2] Univ Bourgogne, CNRS, Inst Math Bourgogne, UMR 5584, BP 47 870, F-21078 Dijon, France

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2016年 / 260卷 / 04期

关键词：

PERTURBATION-THEORY;

D O I：

10.1016/j.jde.2015.10.045

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper studies a slow fast system whose principal characteristic is that the slow manifold is given by the critical set of the cusp catastrophe. Our analysis consists of two main parts: first, we recall a formal normal form suitable for systems as the one studied here; afterwards, taking advantage of this normal form, we investigate the transition near the cusp singularity by means of the blow up technique. Our contribution relies heavily in the usage of normal form theory, allowing us to refine previous results. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：3785 / 3843

页数：59

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