On the stability of homoclinic loops with higher dimension

Xingbo Liu; Deming Zhu

doi:10.3934/dcdsb.2012.17.915

On the stability of homoclinic loops with higher dimension

Xingbo Liu^*
, Deming Zhu

^*Corresponding author for this work

School of Mathematical Sciences

East China Normal University

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

5 Scopus citations

Abstract

In this paper the stability of homoclinic loops of saddle equilibrium states in high dimensional systems is analyzed. By constructing local moving frame along the unperturbed homoclinic orbit, the reffned Poincarffe map is well established, and simple criteria are given for the stability of the saddle homoclinic loop. Some known results are extended.

Original language	English
Pages (from-to)	915-932
Number of pages	18
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	17
Issue number	3
DOIs	https://doi.org/10.3934/dcdsb.2012.17.915
State	Published - May 2012

Keywords

Homoclinic orbits
Moving frame
Stability

Access to Document

10.3934/dcdsb.2012.17.915

Cite this

@article{fc724f62dfd04aefb05da2e1b6dc0c58,

title = "On the stability of homoclinic loops with higher dimension",

abstract = "In this paper the stability of homoclinic loops of saddle equilibrium states in high dimensional systems is analyzed. By constructing local moving frame along the unperturbed homoclinic orbit, the reffned Poincarffe map is well established, and simple criteria are given for the stability of the saddle homoclinic loop. Some known results are extended.",

keywords = "Homoclinic orbits, Moving frame, Stability",

author = "Xingbo Liu and Deming Zhu",

year = "2012",

month = may,

doi = "10.3934/dcdsb.2012.17.915",

language = "英语",

volume = "17",

pages = "915--932",

journal = "Discrete and Continuous Dynamical Systems - Series B",

issn = "1531-3492",

publisher = "American Institute of Mathematical Sciences",

number = "3",

}

TY - JOUR

T1 - On the stability of homoclinic loops with higher dimension

AU - Liu, Xingbo

AU - Zhu, Deming

PY - 2012/5

Y1 - 2012/5

N2 - In this paper the stability of homoclinic loops of saddle equilibrium states in high dimensional systems is analyzed. By constructing local moving frame along the unperturbed homoclinic orbit, the reffned Poincarffe map is well established, and simple criteria are given for the stability of the saddle homoclinic loop. Some known results are extended.

AB - In this paper the stability of homoclinic loops of saddle equilibrium states in high dimensional systems is analyzed. By constructing local moving frame along the unperturbed homoclinic orbit, the reffned Poincarffe map is well established, and simple criteria are given for the stability of the saddle homoclinic loop. Some known results are extended.

KW - Homoclinic orbits

KW - Moving frame

KW - Stability

UR - https://www.scopus.com/pages/publications/84862963833

U2 - 10.3934/dcdsb.2012.17.915

DO - 10.3934/dcdsb.2012.17.915

M3 - 文章

AN - SCOPUS:84862963833

SN - 1531-3492

VL - 17

SP - 915

EP - 932

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 3

ER -

On the stability of homoclinic loops with higher dimension

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this