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

School of Mathematical Sciences

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

7 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	905-916
Number of pages	12
Journal	Chinese Annals of Mathematics. Series B
Volume	32
Issue number	6
DOIs	https://doi.org/10.1007/s11401-011-0675-y
State	Published - Nov 2011

Keywords

Homoclinic orbit
Local coordinate system
Periodic orbit
Poincaré maps
Transcritical bifurcation

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10.1007/s11401-011-0675-y

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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",

publisher = "Springer Verlag",

number = "6",

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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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Keywords

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