Exponential trichotomy and homoclinic bifurcation with saddle-center equilibrium

Xingbo Liu

doi:10.1016/j.aml.2009.11.008

Exponential trichotomy and homoclinic bifurcation with saddle-center equilibrium

Xingbo Liu^*

^*Corresponding author for this work

School of Mathematical Sciences

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

2 Scopus citations

Abstract

In this paper the bifurcation of a homoclinic orbit is studied for an ordinary differential equation with periodic perturbation. Exponential trichotomy theory with the method of Lyapunov-Schmidt is used to obtain some sufficient conditions to guarantee the existence of homoclinic solutions and periodic solutions for this problem. Some known results are extended.

Original language	English
Pages (from-to)	409-416
Number of pages	8
Journal	Applied Mathematics Letters
Volume	23
Issue number	4
DOIs	https://doi.org/10.1016/j.aml.2009.11.008
State	Published - Apr 2010

Keywords

Bifurcation
Exponential trichotomy
Homoclinic orbit
Lyapunov-Schmidt method
Saddle center

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10.1016/j.aml.2009.11.008

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title = "Exponential trichotomy and homoclinic bifurcation with saddle-center equilibrium",

abstract = "In this paper the bifurcation of a homoclinic orbit is studied for an ordinary differential equation with periodic perturbation. Exponential trichotomy theory with the method of Lyapunov-Schmidt is used to obtain some sufficient conditions to guarantee the existence of homoclinic solutions and periodic solutions for this problem. Some known results are extended.",

keywords = "Bifurcation, Exponential trichotomy, Homoclinic orbit, Lyapunov-Schmidt method, Saddle center",

author = "Xingbo Liu",

year = "2010",

month = apr,

doi = "10.1016/j.aml.2009.11.008",

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journal = "Applied Mathematics Letters",

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T1 - Exponential trichotomy and homoclinic bifurcation with saddle-center equilibrium

AU - Liu, Xingbo

PY - 2010/4

Y1 - 2010/4

N2 - In this paper the bifurcation of a homoclinic orbit is studied for an ordinary differential equation with periodic perturbation. Exponential trichotomy theory with the method of Lyapunov-Schmidt is used to obtain some sufficient conditions to guarantee the existence of homoclinic solutions and periodic solutions for this problem. Some known results are extended.

AB - In this paper the bifurcation of a homoclinic orbit is studied for an ordinary differential equation with periodic perturbation. Exponential trichotomy theory with the method of Lyapunov-Schmidt is used to obtain some sufficient conditions to guarantee the existence of homoclinic solutions and periodic solutions for this problem. Some known results are extended.

KW - Bifurcation

KW - Exponential trichotomy

KW - Homoclinic orbit

KW - Lyapunov-Schmidt method

KW - Saddle center

UR - https://www.scopus.com/pages/publications/76749119398

U2 - 10.1016/j.aml.2009.11.008

DO - 10.1016/j.aml.2009.11.008

M3 - 文章

AN - SCOPUS:76749119398

SN - 0893-9659

VL - 23

SP - 409

EP - 416

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 4

ER -

Exponential trichotomy and homoclinic bifurcation with saddle-center equilibrium

Abstract

Keywords

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