Canard Explosion Near Non-Lienard Type Slow-Fast Hopf Point

被引：4
作者：
Huzak, Renato [1 ]
机构：
[1] Hasselt Univ, Campus Diepenbeek,Agoralaan Gebouw D, B-3590 Diepenbeek, Belgium
来源：
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2019年 / 31卷 / 02期
关键词：
Family blow-up; Normal forms; Singular perturbation theory; Slow-fast Hopf point;
D O I：
10.1007/s10884-018-9645-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we study birth of canards near a smooth slow-fast Hopf point of non-Lienard center type which plays an important role in slow-fast codimension 3 saddle and elliptic bifurcations. We show that the number of limit cycles created in the birth of canards in such a slow-fast non-Lienard case is finite. Our paper is also a natural continuation of Dumortier and Roussarie (Discrete Contin Dyn Syst Ser S 2(4):723-781, 2009) where slow-fast Hopf points of Lienard type have been studied. We use geometric singular perturbation theory and the family blow-up.
引用
收藏
页码：683 / 709
页数：27
相关论文
共 11 条
[1]  
[Anonymous], COLLECT MATH
[2]   Cyclicity of common slow-fast cycles [J].
De Maesschalck, P. ;
Dumortier, F. ;
Roussarie, R. .
INDAGATIONES MATHEMATICAE-NEW SERIES, 2011, 22 (3-4) :165-206
[3]  
Dumortier F, 1996, MEM AM MATH SOC, V121, P1
[4]  
Dumortier F., 2010, QUAL THEORY DYN SYST, V9, P39, DOI [DOI 10.1007/S12346-010-0020-Y, 10.1007/s12346-010-0020-y]
[5]   BIRTH OF CANARD CYCLES [J].
Dumortier, Freddy ;
Roussarie, Robert .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2009, 2 (04) :723-781
[6]   Limit cycles in slow-fast codimension 3 saddle and elliptic bifurcations [J].
Huzak, R. ;
De Maesschalck, P. ;
Dumortier, F. .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 255 (11) :4012-4051
[7]  
Huzak R, 2013, THESIS
[8]   NORMAL FORMS OF LIENARD TYPE FOR ANALYTIC UNFOLDINGS OF NILPOTENT SINGULARITIES [J].
Huzak, Renato .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 145 (10) :4325-4336
[9]   CYCLICITY OF THE ORIGIN IN SLOW-FAST CODIMENSION 3 SADDLE AND ELLIPTIC BIFURCATIONS [J].
Huzak, Renato .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2016, 36 (01) :171-215
[10]   PRIMARY BIRTH OF CANARD CYCLES IN SLOW-FAST CODIMENSION 3 ELLIPTIC BIFURCATIONS [J].
Huzak, Renato ;
De Maesschalck, Peter ;
Dumortier, Freddy .
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2014, 13 (06) :2641-2673
12