ANALYSIS OF THE TAKENS-BOGDANOV BIFURCATION ON m-PARAMETERIZED VECTOR FIELDS

被引：30

作者：

Carrillo, Francisco A. ^{[1
]}

Verduzco, Fernando ^{[1
]}

Delgado, Joaquin ^{[2
]}

机构：

[1] Univ Sonora, Dept Matemat, Hermosillo 83000, Sonora, Mexico

[2] Univ Autonoma Metropolitana Iztapalapa, Dept Matemat, Mexico City, DF, Mexico

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2010年 / 20卷 / 04期

关键词：

Takens-Bogdanov bifurcation; center manifold; versal deformation;

D O I：

10.1142/S0218127410026277

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Given an m-parameterized family of n-dimensional vector fields, such that: (i) for some value of the parameters, the family has an equilibrium point, (ii) its linearization has a double zero eigenvalue and no other eigenvalue on the imaginary axis, sufficient conditions on the vector field are given such that the dynamics on the two-dimensional center manifold is locally topologically equivalent to the versal deformation of the planar Takens-Bogdanov bifurcation.

引用

页码：995 / 1005

页数：11

共 8 条

[1]

[Anonymous], 1985, Nauka

[2]

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[3]

BOGDANOV R., 1975, Nonlinear Funct Anal Appl, V9, P144, DOI [10.1007/BF01075453, DOI 10.1007/BF01075453]

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Verduzco, Fernando .

ACTA APPLICANDAE MATHEMATICAE, 2009, 105 (02) :199-225

[5]

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[6]

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[7]

Takens F., 1974, COMMUN MATH I RIJKSU, V3, P1, DOI DOI 10.1201/9781420034288

[8]

Wiggins S., 2003, INTRO APPL NONLINEAR

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