Zero-Hopf bifurcation in the general Van der Pol-Duffing equation

被引：3

作者：

Candido, Murilo R. ^{[1
]}

Valls, Claudia ^{[2
]}

机构：

[1] Univ Estadual Campinas, Dept Matemat, Rua Sergio Baruque de Holanda 651, BR-13083859 Campinas, SP, Brazil

[2] Univ Lisbon, Inst Super Tecn, Dept Matemat, P-1049001 Lisbon, Portugal

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2022年 / 179卷

基金：

巴西圣保罗研究基金会;

关键词：

Invariant tori; Periodic solutions; Averaging method; PERIODIC-SOLUTIONS; SINGULARITIES;

D O I：

10.1016/j.geomphys.2022.104609

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work we study the invariant sets which emerge from the zero-Hopf bifurcations that general Van der Pol-Duffing equations can exhibit. We provide sufficient conditions for the simultaneous bifurcation of three periodic solutions and two invariant torus from the origin of this system. We use recent results related to the averaging method in order to analytically obtain our results. We also provide numerical examples for all the analytical results that we provide. (c) 2022 Elsevier B.V. All rights reserved.

引用

页数：18

共 12 条

[1] Hopf-Zero singularities truly unfold chaos [J].