Homoclinic flip bifurcation with a nonhyperbolic equilibrium

Xingbo Liu; Lina Shi; Dongmei Zhang

doi:10.1007/s11071-011-0294-x

Homoclinic flip bifurcation with a nonhyperbolic equilibrium

Xingbo Liu, Lina Shi, Dongmei Zhang

School of Mathematical Sciences

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

8 Scopus citations

Abstract

In this paper, the problem of homoclinic bifurcation accompanied by a transcritical bifurcation is investigated for high-dimensional systems. With the aid of a suitable local coordinate system, the Poincaré map is constructed. Under certain nongeneric conditions (orbit flip and inclination flip homoclinic orbits), the existence, nonexistence, coexistence and uniqueness of homoclinic and periodic orbits are studied. Some known results are extended.

Original language	English
Pages (from-to)	655-665
Number of pages	11
Journal	Nonlinear Dynamics
Volume	69
Issue number	1-2
DOIs	https://doi.org/10.1007/s11071-011-0294-x
State	Published - Jul 2012

Keywords

Homoclinic bifurcation
Inclination flip
Local coordinates
Orbit flip
Transcritical bifurcation

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10.1007/s11071-011-0294-x

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title = "Homoclinic flip bifurcation with a nonhyperbolic equilibrium",

abstract = "In this paper, the problem of homoclinic bifurcation accompanied by a transcritical bifurcation is investigated for high-dimensional systems. With the aid of a suitable local coordinate system, the Poincar{\'e} map is constructed. Under certain nongeneric conditions (orbit flip and inclination flip homoclinic orbits), the existence, nonexistence, coexistence and uniqueness of homoclinic and periodic orbits are studied. Some known results are extended.",

keywords = "Homoclinic bifurcation, Inclination flip, Local coordinates, Orbit flip, Transcritical bifurcation",

author = "Xingbo Liu and Lina Shi and Dongmei Zhang",

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AU - Liu, Xingbo

AU - Shi, Lina

AU - Zhang, Dongmei

PY - 2012/7

Y1 - 2012/7

N2 - In this paper, the problem of homoclinic bifurcation accompanied by a transcritical bifurcation is investigated for high-dimensional systems. With the aid of a suitable local coordinate system, the Poincaré map is constructed. Under certain nongeneric conditions (orbit flip and inclination flip homoclinic orbits), the existence, nonexistence, coexistence and uniqueness of homoclinic and periodic orbits are studied. Some known results are extended.

AB - In this paper, the problem of homoclinic bifurcation accompanied by a transcritical bifurcation is investigated for high-dimensional systems. With the aid of a suitable local coordinate system, the Poincaré map is constructed. Under certain nongeneric conditions (orbit flip and inclination flip homoclinic orbits), the existence, nonexistence, coexistence and uniqueness of homoclinic and periodic orbits are studied. Some known results are extended.

KW - Homoclinic bifurcation

KW - Inclination flip

KW - Local coordinates

KW - Orbit flip

KW - Transcritical bifurcation

UR - https://www.scopus.com/pages/publications/84861726466

U2 - 10.1007/s11071-011-0294-x

DO - 10.1007/s11071-011-0294-x

M3 - 文章

AN - SCOPUS:84861726466

SN - 0924-090X

VL - 69

SP - 655

EP - 665

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

IS - 1-2

ER -

Homoclinic flip bifurcation with a nonhyperbolic equilibrium

Abstract

Keywords

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