Stability of singular Hopf bifurcations

被引：7

作者：

Yang, LJ ^{[1
]}

Zeng, XW

机构：

[1] Tsing Hua Univ, Dept Math Sci, Beijing 100084, Peoples R China

[2] Wuhan Univ, Dept Math, Wuhan 430072, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2004年 / 206卷 / 01期

基金：

中国国家自然科学基金;

关键词：

singular Hopf bifurcation; singularly perturbed system; Lyapunov constant; stability constant; stability formula;

D O I：

10.1016/j.jde.2004.08.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A stability formula is given for the singular Hopf bifurcation arising in singularly perturbed systems of the form (x)over dot = epsilonf (x, y, lambda), (y)over dot = g(x, y, lambda) in this paper. The derivation of the formula is based on a reduction technique and on an existing stability formula for Hopf bifurcation. (C) 2004 Elsevier Inc. All rights reserved.

引用

页码：30 / 54

页数：25

共 50 条

[31] Hopf bifurcations and homoclinic tangencies
Martín, JC
NONLINEARITY, 1999, 12 (04) : 893 - 902
[32] Controlling degenerate Hopf bifurcations
Moiola, JL
Berns, DW
Chen, GR
LATIN AMERICAN APPLIED RESEARCH, 1999, 29 (3-4) : 213 - 220
[33] HOPF BIFURCATIONS IN LANGMUIR CIRCULATIONS
COX, SM
LEIBOVICH, S
MOROZ, IM
TANDON, A
PHYSICA D, 1992, 59 (1-3): : 226 - 254
[34] Hopf bifurcations in dynamical systems
Salvatore Rionero
Ricerche di Matematica, 2019, 68 : 811 - 840
[35] Analysis and control of Hopf bifurcations
Hamzi, B
Kang, W
Barbot, JP
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2004, 42 (06) : 2200 - 2220
[36] Control of dynamic Hopf bifurcations
Berglund, N
NONLINEARITY, 2000, 13 (01) : 225 - 248
[37] Hopf bifurcations on cubic lattices
Callahan, TK
BIFURCATION, SYMMETRY AND PATTERNS, 2003, : 123 - 127
[38] Hopf bifurcations with fluctuating gain
Triana, S. A.
Kelley, D. H.
Zimmerman, D.
Sisan, D.
Lathrop, D. P.
ASTRONOMISCHE NACHRICHTEN, 2008, 329 (07) : 701 - 705
[39] Discretizing dynamical systems with Hopf-Hopf bifurcations
Paez Chavez, Joseph
IMA JOURNAL OF NUMERICAL ANALYSIS, 2012, 32 (01) : 185 - 201
[40] Hopf bifurcations on cubic lattices
Callahan, TK
NONLINEARITY, 2003, 16 (06) : 2099 - 2122

← 1 2 3 4 5 →