The Hopf bifurcation in the Shimizu-Morioka system

被引：13
|
作者：
Llibre, Jaume [1 ]
Pessoa, Claudio [2 ]
机构：
[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia, Spain
[2] Univ Estadual Paulista, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil
来源：
NONLINEAR DYNAMICS | 2015年 / 79卷 / 03期
基金：
巴西圣保罗研究基金会;
关键词：
Hopf bifurcation; Limit cycles; Bifurcation diagram;
D O I：
10.1007/s11071-014-1805-3
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
We study the local Hopf bifurcations of codimension one and two, which occur in the Shimizu-Morioka system. This system is a simplified model proposed for studying the dynamics of the well-known Lorenz system for large Rayleigh numbers. We present an analytic study and their bifurcation diagrams of these kinds of Hopf bifurcation, showing the qualitative changes in the dynamics of its solutions for different values of the parameters.
引用
收藏
页码：2197 / 2205
页数：9
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