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Homoclinic Bifurcations in Planar Piecewise-Linear Systems
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| Zeitschriftentitel: | Discrete Dynamics in Nature and Society |
|---|---|
| Personen und Körperschaften: | , , , |
| In: | Discrete Dynamics in Nature and Society, 2013, 2013, S. 1-9 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
Hindawi Limited
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| Schlagwörter: |
| author_facet |
Xu, Bin Yang, Fenghong Tang, Yun Lin, Mu Xu, Bin Yang, Fenghong Tang, Yun Lin, Mu |
|---|---|
| author |
Xu, Bin Yang, Fenghong Tang, Yun Lin, Mu |
| spellingShingle |
Xu, Bin Yang, Fenghong Tang, Yun Lin, Mu Discrete Dynamics in Nature and Society Homoclinic Bifurcations in Planar Piecewise-Linear Systems Modeling and Simulation |
| author_sort |
xu, bin |
| spelling |
Xu, Bin Yang, Fenghong Tang, Yun Lin, Mu 1026-0226 1607-887X Hindawi Limited Modeling and Simulation http://dx.doi.org/10.1155/2013/732321 <jats:p>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.</jats:p> Homoclinic Bifurcations in Planar Piecewise-Linear Systems Discrete Dynamics in Nature and Society |
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Hindawi Limited, 2013 |
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Discrete Dynamics in Nature and Society |
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49 |
| title |
Homoclinic Bifurcations in Planar Piecewise-Linear Systems |
| title_unstemmed |
Homoclinic Bifurcations in Planar Piecewise-Linear Systems |
| title_full |
Homoclinic Bifurcations in Planar Piecewise-Linear Systems |
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Homoclinic Bifurcations in Planar Piecewise-Linear Systems |
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Homoclinic Bifurcations in Planar Piecewise-Linear Systems |
| title_short |
Homoclinic Bifurcations in Planar Piecewise-Linear Systems |
| title_sort |
homoclinic bifurcations in planar piecewise-linear systems |
| topic |
Modeling and Simulation |
| url |
http://dx.doi.org/10.1155/2013/732321 |
| publishDate |
2013 |
| physical |
1-9 |
| description |
<jats:p>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.</jats:p> |
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| author | Xu, Bin, Yang, Fenghong, Tang, Yun, Lin, Mu |
| author_facet | Xu, Bin, Yang, Fenghong, Tang, Yun, Lin, Mu, Xu, Bin, Yang, Fenghong, Tang, Yun, Lin, Mu |
| author_sort | xu, bin |
| container_start_page | 1 |
| container_title | Discrete Dynamics in Nature and Society |
| container_volume | 2013 |
| description | <jats:p>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.</jats:p> |
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| imprint | Hindawi Limited, 2013 |
| imprint_str_mv | Hindawi Limited, 2013 |
| institution | DE-Brt1, DE-D161, DE-Zwi2, DE-Gla1, DE-Zi4, DE-15, DE-Pl11, DE-Rs1, DE-105, DE-14, DE-Ch1, DE-L229, DE-D275, DE-Bn3 |
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| series | Discrete Dynamics in Nature and Society |
| source_id | 49 |
| spelling | Xu, Bin Yang, Fenghong Tang, Yun Lin, Mu 1026-0226 1607-887X Hindawi Limited Modeling and Simulation http://dx.doi.org/10.1155/2013/732321 <jats:p>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.</jats:p> Homoclinic Bifurcations in Planar Piecewise-Linear Systems Discrete Dynamics in Nature and Society |
| spellingShingle | Xu, Bin, Yang, Fenghong, Tang, Yun, Lin, Mu, Discrete Dynamics in Nature and Society, Homoclinic Bifurcations in Planar Piecewise-Linear Systems, Modeling and Simulation |
| title | Homoclinic Bifurcations in Planar Piecewise-Linear Systems |
| title_full | Homoclinic Bifurcations in Planar Piecewise-Linear Systems |
| title_fullStr | Homoclinic Bifurcations in Planar Piecewise-Linear Systems |
| title_full_unstemmed | Homoclinic Bifurcations in Planar Piecewise-Linear Systems |
| title_short | Homoclinic Bifurcations in Planar Piecewise-Linear Systems |
| title_sort | homoclinic bifurcations in planar piecewise-linear systems |
| title_unstemmed | Homoclinic Bifurcations in Planar Piecewise-Linear Systems |
| topic | Modeling and Simulation |
| url | http://dx.doi.org/10.1155/2013/732321 |