Codimension-3 bifurcations of a class of homoclinic loop with saddle-point

In this work, bifurcations in the class that the homoclinic orbit connects the strong stable and strong unstable manifolds of a saddle are investigated for four-dimensional vector fields. The existence, numbers, coexistence and incoexistence of 1-homoclinic orbit, 1-periodic orbit, 2 n -homoclinic o...

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Bibliographic Details
Published inNonlinear analysis Vol. 69; no. 11; pp. 3761 - 3773
Main Authors Deng, Guifeng, Zhu, Deming
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Ltd 01.12.2008
Elsevier
Subjects
34C23
34C28
34C37
Exact sciences and technology
Global analysis, analysis on manifolds
Homoclinic orbit
Mathematical analysis
Mathematics
Nonleading eigendirection
Ordinary differential equations
Periodic orbit
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Periodic orbit
34C37
Nonleading eigendirection
34C23
Homoclinic orbit
34C28
Stable manifold
Nonlinear analysis
Bifurcation
Mathematical model
Vector field
Surface
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Summary:In this work, bifurcations in the class that the homoclinic orbit connects the strong stable and strong unstable manifolds of a saddle are investigated for four-dimensional vector fields. The existence, numbers, coexistence and incoexistence of 1-homoclinic orbit, 1-periodic orbit, 2 n -homoclinic orbit and 2 n -periodic orbit are obtained, the approximate expressions of the corresponding bifurcation surfaces and the bifurcation diagrams are also presented.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2007.10.013