Regular and slow-fast codimension 4 saddle-node bifurcations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:262

Article

Huzak, Renato¹ 

[1] Hasselt Univ, Campus Diepenbeek,Agoralaan Gebouw D, B-3590 Diepenbeek, Belgium

关键词: Blow-up;    Limit cycles;    Singular perturbations;    Slow-fast systems;   

DOI  :  10.1016/j.jde.2016.10.008

来源: Elsevier

【 摘 要 】

Using geometric singular perturbation theory, including the family blow-up as one of the main techniques, we prove that the cyclicity, i.e. maximum number of limit cycles, in both regular and slow-fast unfoldings of nilpotent saddle-node singularity of codimension 4 is 2. The blow-up technique enables us to use the well known results for slow-fast codimension 1 and 2 Hopf bifurcations, slow-fast Bogdanov- Takens bifurcations and slow-fast codimension 3 saddle and elliptic bifurcations. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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