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Bifurcation of Nongeneric Homoclinic Orbit Accompanied by Pitchfork Bifurcation
Joint Authors
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-04-07
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
The bifurcation of a nongeneric homoclinic orbit (i.e., the orbit comes from the equilibrium along the unstable manifold instead of the center manifold) connecting a nonhyperbolic equilibrium is investigated, and the nonhyperbolic equilibrium undergoes a pitchfork bifurcation.
The existence (resp., nonexistence) of a homoclinic orbit and an 1-periodic orbit are established when the pitchfork bifurcation does not happen, while as the nonhyperbolic equilibrium undergoes a pitchfork bifurcation, we obtain the sufficient conditions for the existence of homoclinic orbit and two or three heteroclinic orbits, and so forth.
Moreover, we explore the difference between the bifurcation of the nongeneric homoclinic orbit and the generic one.
American Psychological Association (APA)
Geng, Fengjie& Li, Song. 2014. Bifurcation of Nongeneric Homoclinic Orbit Accompanied by Pitchfork Bifurcation. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-7.
https://search.emarefa.net/detail/BIM-1013462
Modern Language Association (MLA)
Geng, Fengjie& Li, Song. Bifurcation of Nongeneric Homoclinic Orbit Accompanied by Pitchfork Bifurcation. Abstract and Applied Analysis No. 2014 (2014), pp.1-7.
https://search.emarefa.net/detail/BIM-1013462
American Medical Association (AMA)
Geng, Fengjie& Li, Song. Bifurcation of Nongeneric Homoclinic Orbit Accompanied by Pitchfork Bifurcation. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-7.
https://search.emarefa.net/detail/BIM-1013462
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1013462