On the Hopf-zero bifurcation of the Michelson system

被引：21
|
作者：
Llibre, Jaume [1 ]
Zhang, Xiang [2 ]
机构：
[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Spain
[2] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China
来源：
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2011年 / 12卷 / 03期
关键词：
Michelson system; Periodic orbit; Averaging method; Hopf bifurcation; STEADY SOLUTIONS;
D O I：
10.1016/j.nonrwa.2010.10.019
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Applying a new result for studying the periodic orbits of a differential system via the averaging theory, we provide the first analytic proof of the existence of a Hopf-zero bifurcation for the Michelson system (x) over dot = y, (y) over dot = z, (z) over dot = c(2) - y - x(2)/2, at c = 0. Moreover our method estimates the shape of this periodic orbit as a function of c > 0, sufficiently small. (C) 2010 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1650 / 1653
页数：4
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