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

页码：1650 / 1653

页数：4

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