Loop Numbers for the Stability of Homoclinic Loops of Planar Vector Fields

Xingbo Liu; Xiao Biao Lin; Yuzhen Bai; Deming Zhu

doi:10.1142/S0218127418501018

Loop Numbers for the Stability of Homoclinic Loops of Planar Vector Fields

Xingbo Liu
, Xiao Biao Lin
, Yuzhen Bai
, Deming Zhu

数学科学学院

North Carolina State University
Qufu Normal University
East China Normal University

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

This paper is devoted to the study of stability and bifurcations of homoclinic loops for planar vector fields. For a given homoclinic loop, a sequence of loop numbers can be defined such that the stability and bifurcations of the loop are determined by the first nonzero term of the sequence. Formulas for the first several loop numbers were established in the past. In this paper, we will introduce general formulas for the loop numbers for both the single and double homoclinic loops.

源语言	英语
文章编号	1850101
期刊	International Journal of Bifurcation and Chaos
卷	28
期	8
DOI	https://doi.org/10.1142/S0218127418501018
出版状态	已出版 - 1 7月 2018

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abstract = "This paper is devoted to the study of stability and bifurcations of homoclinic loops for planar vector fields. For a given homoclinic loop, a sequence of loop numbers can be defined such that the stability and bifurcations of the loop are determined by the first nonzero term of the sequence. Formulas for the first several loop numbers were established in the past. In this paper, we will introduce general formulas for the loop numbers for both the single and double homoclinic loops.",

keywords = "Homoclinic loops, Poincar{\'e} return map, bifurcation, local moving frame, stability",

author = "Xingbo Liu and Lin, \{Xiao Biao\} and Yuzhen Bai and Deming Zhu",

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AU - Liu, Xingbo

AU - Lin, Xiao Biao

AU - Bai, Yuzhen

AU - Zhu, Deming

PY - 2018/7/1

Y1 - 2018/7/1

N2 - This paper is devoted to the study of stability and bifurcations of homoclinic loops for planar vector fields. For a given homoclinic loop, a sequence of loop numbers can be defined such that the stability and bifurcations of the loop are determined by the first nonzero term of the sequence. Formulas for the first several loop numbers were established in the past. In this paper, we will introduce general formulas for the loop numbers for both the single and double homoclinic loops.

AB - This paper is devoted to the study of stability and bifurcations of homoclinic loops for planar vector fields. For a given homoclinic loop, a sequence of loop numbers can be defined such that the stability and bifurcations of the loop are determined by the first nonzero term of the sequence. Formulas for the first several loop numbers were established in the past. In this paper, we will introduce general formulas for the loop numbers for both the single and double homoclinic loops.

KW - Homoclinic loops

KW - Poincaré return map

KW - bifurcation

KW - local moving frame

KW - stability

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VL - 28

JO - International Journal of Bifurcation and Chaos

JF - International Journal of Bifurcation and Chaos

IS - 8

M1 - 1850101

ER -

Loop Numbers for the Stability of Homoclinic Loops of Planar Vector Fields

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