Resonant 1:2 double Hopf bifurcation in an oscillator with delayed feedback

被引：5

作者：

Gentile, F. S. ^{[1
]}

Itovich, G. R. ^{[2
]}

Moiola, J. L. ^{[3
]}

机构：

[1] Univ Nacl Sur, Dept Matemat, IIIE, UNS CONICET, B8000CPB, Bahia Blanca, Buenos Aires, Argentina

[2] Univ Nacl Rio Negro, Escuela Prod Tecnol & Medio Ambiente, Sede Alto Valle, R8336ATG, Villa Regina, Argentina

[3] Univ Nacl Sur, Dept Ingn Elect & Comp, IIIE, UNS CONICET, B8000CPB, Bahia Blanca, Buenos Aires, Argentina

来源：

NONLINEAR DYNAMICS | 2018年 / 91卷 / 03期

关键词：

Time-delay systems; Graphical Hopf theorem; 1:2 resonance; SYSTEMS;

D O I：

10.1007/s11071-017-3980-5

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

In this work, the dynamics of an oscillator with delayed feedback is analyzed. It is found that for certain values of the parameters, the system exhibits a phenomenon known as double Hopf bifurcation with 1:2 resonance. This singularity provokes the interaction between two oscillatory solutions, one of frequency and the other with frequency . By using the graphical Hopf bifurcation theorem, the system dynamics in a neighborhood of this singularity is explored. Also, with the aid of the package DDE-Biftool, some global bifurcations are detected in order to provide a better understanding of the whole scenario.

引用

页码：1779 / 1789

页数：11

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