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Bifurcations and Stability of Nondegenerated Homoclinic Loops for Higher Dimensional Systems
Joint Authors
Li, Feng
Jin, Yinlai
Xu, Han
Zhang, Liqun
Li, Jing
Ding, Benyan
Source
Computational and Mathematical Methods in Medicine
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-11-12
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
By using the foundational solutions of the linear variational equation of the unperturbed system along the homoclinic orbit as the local current coordinates system of the system in the small neighborhood of the homoclinic orbit, we discuss the bifurcation problems of nondegenerated homoclinic loops.
Under the nonresonant condition, existence, uniqueness, and incoexistence of 1-homoclinic loop and 1-periodic orbit, the inexistence of k-homoclinic loop and k-periodic orbit is obtained.
Under the resonant condition, we study the existence of 1-homoclinic loop, 1-periodic orbit, 2-fold 1-periodic orbit, and two 1-periodic orbits; the coexistence of 1-homoclinic loop and 1-periodic orbit.
Moreover, we give the corresponding existence fields and bifurcation surfaces.
At last, we study the stability of the homoclinic loop for the two cases of non-resonant and resonant, and we obtain the corresponding criterions.
American Psychological Association (APA)
Jin, Yinlai& Li, Feng& Xu, Han& Li, Jing& Zhang, Liqun& Ding, Benyan. 2013. Bifurcations and Stability of Nondegenerated Homoclinic Loops for Higher Dimensional Systems. Computational and Mathematical Methods in Medicine،Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-482632
Modern Language Association (MLA)
Jin, Yinlai…[et al.]. Bifurcations and Stability of Nondegenerated Homoclinic Loops for Higher Dimensional Systems. Computational and Mathematical Methods in Medicine No. 2013 (2013), pp.1-9.
https://search.emarefa.net/detail/BIM-482632
American Medical Association (AMA)
Jin, Yinlai& Li, Feng& Xu, Han& Li, Jing& Zhang, Liqun& Ding, Benyan. Bifurcations and Stability of Nondegenerated Homoclinic Loops for Higher Dimensional Systems. Computational and Mathematical Methods in Medicine. 2013. Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-482632
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-482632