Homoclinic flip bifurcations accompanied by transcritical bifurcation

Xingbo Liu

doi:10.1007/s11401-011-0675-y

Homoclinic flip bifurcations accompanied by transcritical bifurcation

Xingbo Liu^*

^*此作品的通讯作者

数学科学学院

科研成果: 期刊稿件 › 文章 › 同行评审

7 引用（Scopus）

摘要

The bifurcations of orbit flip homoclinic loop with nonhyperbolic equilibria are investigated. By constructing local coordinate systems near the unperturbed homoclinic orbit, Poincaré maps for the new system are established. Then the existence of homoclinic orbit and the periodic orbit is studied for the system accompanied with transcritical bifurcation.

源语言	英语
页（从-至）	905-916
页数	12
期刊	Chinese Annals of Mathematics. Series B
卷	32
期	6
DOI	https://doi.org/10.1007/s11401-011-0675-y
出版状态	已出版 - 11月 2011

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10.1007/s11401-011-0675-y

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@article{51e1f3748fb246ca93cacae2879e0dd8,

title = "Homoclinic flip bifurcations accompanied by transcritical bifurcation",

abstract = "The bifurcations of orbit flip homoclinic loop with nonhyperbolic equilibria are investigated. By constructing local coordinate systems near the unperturbed homoclinic orbit, Poincar{\'e} maps for the new system are established. Then the existence of homoclinic orbit and the periodic orbit is studied for the system accompanied with transcritical bifurcation.",

keywords = "Homoclinic orbit, Local coordinate system, Periodic orbit, Poincar{\'e} maps, Transcritical bifurcation",

author = "Xingbo Liu",

year = "2011",

month = nov,

doi = "10.1007/s11401-011-0675-y",

language = "英语",

volume = "32",

pages = "905--916",

journal = "Chinese Annals of Mathematics. Series B",

issn = "0252-9599",

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TY - JOUR

T1 - Homoclinic flip bifurcations accompanied by transcritical bifurcation

AU - Liu, Xingbo

PY - 2011/11

Y1 - 2011/11

N2 - The bifurcations of orbit flip homoclinic loop with nonhyperbolic equilibria are investigated. By constructing local coordinate systems near the unperturbed homoclinic orbit, Poincaré maps for the new system are established. Then the existence of homoclinic orbit and the periodic orbit is studied for the system accompanied with transcritical bifurcation.

AB - The bifurcations of orbit flip homoclinic loop with nonhyperbolic equilibria are investigated. By constructing local coordinate systems near the unperturbed homoclinic orbit, Poincaré maps for the new system are established. Then the existence of homoclinic orbit and the periodic orbit is studied for the system accompanied with transcritical bifurcation.

KW - Homoclinic orbit

KW - Local coordinate system

KW - Periodic orbit

KW - Poincaré maps

KW - Transcritical bifurcation

UR - https://www.scopus.com/pages/publications/80455143370

U2 - 10.1007/s11401-011-0675-y

DO - 10.1007/s11401-011-0675-y

M3 - 文章

AN - SCOPUS:80455143370

SN - 0252-9599

VL - 32

SP - 905

EP - 916

JO - Chinese Annals of Mathematics. Series B

JF - Chinese Annals of Mathematics. Series B

IS - 6

ER -

Homoclinic flip bifurcations accompanied by transcritical bifurcation

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