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
收藏
页码：1779 / 1789
页数：11
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