Homoclinic Bifurcations in Planar Piecewise-Linear Systems
Joint Authors
Lin, Mu
Yang, Fenghong
Xu, Bin
Tang, Yun
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-10-26
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
The problem of homoclinic bifurcations in planar continuous piecewise-linear systems with two zones is studied.
This is accomplished by investigating the existence of homoclinic orbits in the systems.
The systems with homoclinic orbits can be divided into two cases: the visible saddle-focus (or saddle-center) case and the case of twofold nodes with opposite stability.
Necessary and sufficient conditions for the existence of homoclinic orbits are provided for further study of homoclinic bifurcations.
Two kinds of homoclinic bifurcations are discussed: one is generically related to nondegenerate homoclinic orbits; the other is the discontinuity induced homoclinic bifurcations related to the boundary.
The results show that at least two parameters are needed to unfold all possible homoclinc bifurcations in the systems.
American Psychological Association (APA)
Xu, Bin& Yang, Fenghong& Tang, Yun& Lin, Mu. 2013. Homoclinic Bifurcations in Planar Piecewise-Linear Systems. Discrete Dynamics in Nature and Society،Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-494293
Modern Language Association (MLA)
Xu, Bin…[et al.]. Homoclinic Bifurcations in Planar Piecewise-Linear Systems. Discrete Dynamics in Nature and Society No. 2013 (2013), pp.1-9.
https://search.emarefa.net/detail/BIM-494293
American Medical Association (AMA)
Xu, Bin& Yang, Fenghong& Tang, Yun& Lin, Mu. Homoclinic Bifurcations in Planar Piecewise-Linear Systems. Discrete Dynamics in Nature and Society. 2013. Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-494293
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-494293
