Bifurcations of Nontwisted Heteroclinic Loop with Resonant Eigenvalues
By using the foundational solutions of the linear variational equation of the unperturbed system along the heteroclinic orbits to establish the local coordinate systems in the small tubular neighborhoods of the heteroclinic orbits, we study the bifurcation problems of nontwisted heteroclinic loop wi...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/716082 |
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| _version_ | 1832562856184250368 |
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| author | Yinlai Jin Xiaowei Zhu Zheng Guo Han Xu Liqun Zhang Benyan Ding |
| author_facet | Yinlai Jin Xiaowei Zhu Zheng Guo Han Xu Liqun Zhang Benyan Ding |
| author_sort | Yinlai Jin |
| collection | DOAJ |
| description | By using the foundational solutions of the linear variational equation of the unperturbed system along the heteroclinic orbits to establish the local
coordinate systems in the small tubular neighborhoods of the
heteroclinic orbits, we study the bifurcation problems of
nontwisted heteroclinic loop with resonant eigenvalues. The
existence, numbers, and existence regions of 1-heteroclinic loop,
1-homoclinic loop, 1-periodic orbit, 2-fold 1-periodic orbit, and two
1-periodic orbits are obtained. Meanwhile, we give the
corresponding bifurcation surfaces. |
| format | Article |
| id | doaj-art-11fd3de31459469cb04d856eb8a4a837 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-11fd3de31459469cb04d856eb8a4a8372025-02-03T01:21:31ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/716082716082Bifurcations of Nontwisted Heteroclinic Loop with Resonant EigenvaluesYinlai Jin0Xiaowei Zhu1Zheng Guo2Han Xu3Liqun Zhang4Benyan Ding5School of Science, Linyi University, Linyi, Shandong 276005, ChinaSchool of Science, Linyi University, Linyi, Shandong 276005, ChinaSchool of Science, Linyi University, Linyi, Shandong 276005, ChinaSchool of Science, Linyi University, Linyi, Shandong 276005, ChinaSchool of Science, Linyi University, Linyi, Shandong 276005, ChinaSchool of Science, Linyi University, Linyi, Shandong 276005, ChinaBy using the foundational solutions of the linear variational equation of the unperturbed system along the heteroclinic orbits to establish the local coordinate systems in the small tubular neighborhoods of the heteroclinic orbits, we study the bifurcation problems of nontwisted heteroclinic loop with resonant eigenvalues. The existence, numbers, and existence regions of 1-heteroclinic loop, 1-homoclinic loop, 1-periodic orbit, 2-fold 1-periodic orbit, and two 1-periodic orbits are obtained. Meanwhile, we give the corresponding bifurcation surfaces.http://dx.doi.org/10.1155/2014/716082 |
| spellingShingle | Yinlai Jin Xiaowei Zhu Zheng Guo Han Xu Liqun Zhang Benyan Ding Bifurcations of Nontwisted Heteroclinic Loop with Resonant Eigenvalues The Scientific World Journal |
| title | Bifurcations of Nontwisted Heteroclinic Loop with Resonant Eigenvalues |
| title_full | Bifurcations of Nontwisted Heteroclinic Loop with Resonant Eigenvalues |
| title_fullStr | Bifurcations of Nontwisted Heteroclinic Loop with Resonant Eigenvalues |
| title_full_unstemmed | Bifurcations of Nontwisted Heteroclinic Loop with Resonant Eigenvalues |
| title_short | Bifurcations of Nontwisted Heteroclinic Loop with Resonant Eigenvalues |
| title_sort | bifurcations of nontwisted heteroclinic loop with resonant eigenvalues |
| url | http://dx.doi.org/10.1155/2014/716082 |
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