Homoclinic bifurcation with nonhyperbolic equilibria

Xingbo Liu; Xianlong Fu; Deming Zhu

doi:10.1016/j.na.2006.04.014

Homoclinic bifurcation with nonhyperbolic equilibria

Xingbo Liu^*, Xianlong Fu, Deming Zhu

^*Corresponding author for this work

School of Mathematical Sciences

East China Normal University

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

The problem of homoclinic bifurcation is studied for a high dimensional system with nonhyperbolic equilibria. By constructing local coordinate systems near the unperturbed homoclinic orbit, Poincaré maps for the new system are established. Then the persistence of the homoclinic orbit and the bifurcation of the periodic orbit for the system accompanied with pitchfork bifurcation are obtained. Some known results are extended.

Original language	English
Pages (from-to)	2931-2939
Number of pages	9
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	66
Issue number	12
DOIs	https://doi.org/10.1016/j.na.2006.04.014
State	Published - 15 Jun 2007

Keywords

34C23
34C37
37C29
Homoclinic orbit
Local coordinate system
Periodic orbit
Pitchfork bifurcation

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10.1016/j.na.2006.04.014

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title = "Homoclinic bifurcation with nonhyperbolic equilibria",

abstract = "The problem of homoclinic bifurcation is studied for a high dimensional system with nonhyperbolic equilibria. By constructing local coordinate systems near the unperturbed homoclinic orbit, Poincar{\'e} maps for the new system are established. Then the persistence of the homoclinic orbit and the bifurcation of the periodic orbit for the system accompanied with pitchfork bifurcation are obtained. Some known results are extended.",

keywords = "34C23, 34C37, 37C29, Homoclinic orbit, Local coordinate system, Periodic orbit, Pitchfork bifurcation",

author = "Xingbo Liu and Xianlong Fu and Deming Zhu",

year = "2007",

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day = "15",

doi = "10.1016/j.na.2006.04.014",

language = "英语",

volume = "66",

pages = "2931--2939",

journal = "Nonlinear Analysis, Theory, Methods and Applications",

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TY - JOUR

T1 - Homoclinic bifurcation with nonhyperbolic equilibria

AU - Liu, Xingbo

AU - Fu, Xianlong

AU - Zhu, Deming

PY - 2007/6/15

Y1 - 2007/6/15

N2 - The problem of homoclinic bifurcation is studied for a high dimensional system with nonhyperbolic equilibria. By constructing local coordinate systems near the unperturbed homoclinic orbit, Poincaré maps for the new system are established. Then the persistence of the homoclinic orbit and the bifurcation of the periodic orbit for the system accompanied with pitchfork bifurcation are obtained. Some known results are extended.

AB - The problem of homoclinic bifurcation is studied for a high dimensional system with nonhyperbolic equilibria. By constructing local coordinate systems near the unperturbed homoclinic orbit, Poincaré maps for the new system are established. Then the persistence of the homoclinic orbit and the bifurcation of the periodic orbit for the system accompanied with pitchfork bifurcation are obtained. Some known results are extended.

KW - 34C23

KW - 34C37

KW - 37C29

KW - Homoclinic orbit

KW - Local coordinate system

KW - Periodic orbit

KW - Pitchfork bifurcation

UR - https://www.scopus.com/pages/publications/33947157232

U2 - 10.1016/j.na.2006.04.014

DO - 10.1016/j.na.2006.04.014

M3 - 文章

AN - SCOPUS:33947157232

SN - 0362-546X

VL - 66

SP - 2931

EP - 2939

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 12

ER -

Homoclinic bifurcation with nonhyperbolic equilibria

Abstract

Keywords

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