Lyapunov coefficients for an invisible fold-fold singularity in planar piecewise Hamiltonian systems

被引：10

作者：

Braga, Denis de Carvalho ^{[1
]}

da Fonseca, Alexander Fernandes ^{[1
]}

Goncalves, Luiz Fernando ^{[2
]}

Mello, Luis Fernando ^{[1
]}

机构：

[1] Univ Fed Itajuba, Inst Matemat & Comp, Ave BPS 1303, BR-37500903 Itajuba, MG, Brazil

[2] UNESP, Inst Biociencias Letras & Ciencias Exatas, Rua Cristovao Colombo 2265, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2020年 / 484卷 / 01期

关键词：

Piecewise smooth vector field; Fold-fold singularity; Bifurcation; Limit cycle; Hamiltonian vector field; BIFURCATIONS;

D O I：

10.1016/j.jmaa.2019.123692

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the stability of an invisible fold-fold singularity of planar piecewise smooth Hamiltonian vector fields by computing some kind of Lyapunov coefficients. We obtain the general expressions for the first five Lyapunov coefficients. As a consequence, the bifurcation diagrams, illustrating the number, types and positions of the bifurcating small amplitude crossing limit cycles for these vector fields, are determined. @ 2019 Elsevier Inc. All rights reserved.

引用

页数：19

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