A High-Order Melnikov Method for Heteroclinic Orbits in Planar Vector Fields and Heteroclinic Persisting Perturbations
This work extends the high-order Melnikov method established by FJ Chen and QD Wang to heteroclinic orbits, and it is used to prove, under a certain class of perturbations, the heteroclinic orbit in a planar vector field that remains unbroken. Perturbations which have this property together form the...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/5140694 |
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| _version_ | 1832565662581522432 |
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| author | Yi Zhong |
| author_facet | Yi Zhong |
| author_sort | Yi Zhong |
| collection | DOAJ |
| description | This work extends the high-order Melnikov method established by FJ Chen and QD Wang to heteroclinic orbits, and it is used to prove, under a certain class of perturbations, the heteroclinic orbit in a planar vector field that remains unbroken. Perturbations which have this property together form the heteroclinic persisting space. The Van der Pol system is analysed as an application. |
| format | Article |
| id | doaj-art-9de555451bdb4a818f2eb1c73357caee |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-9de555451bdb4a818f2eb1c73357caee2025-02-03T01:07:07ZengWileyJournal of Mathematics2314-47852021-01-01202110.1155/2021/5140694A High-Order Melnikov Method for Heteroclinic Orbits in Planar Vector Fields and Heteroclinic Persisting PerturbationsYi Zhong0School of Mathematical SciencesThis work extends the high-order Melnikov method established by FJ Chen and QD Wang to heteroclinic orbits, and it is used to prove, under a certain class of perturbations, the heteroclinic orbit in a planar vector field that remains unbroken. Perturbations which have this property together form the heteroclinic persisting space. The Van der Pol system is analysed as an application.http://dx.doi.org/10.1155/2021/5140694 |
| spellingShingle | Yi Zhong A High-Order Melnikov Method for Heteroclinic Orbits in Planar Vector Fields and Heteroclinic Persisting Perturbations Journal of Mathematics |
| title | A High-Order Melnikov Method for Heteroclinic Orbits in Planar Vector Fields and Heteroclinic Persisting Perturbations |
| title_full | A High-Order Melnikov Method for Heteroclinic Orbits in Planar Vector Fields and Heteroclinic Persisting Perturbations |
| title_fullStr | A High-Order Melnikov Method for Heteroclinic Orbits in Planar Vector Fields and Heteroclinic Persisting Perturbations |
| title_full_unstemmed | A High-Order Melnikov Method for Heteroclinic Orbits in Planar Vector Fields and Heteroclinic Persisting Perturbations |
| title_short | A High-Order Melnikov Method for Heteroclinic Orbits in Planar Vector Fields and Heteroclinic Persisting Perturbations |
| title_sort | high order melnikov method for heteroclinic orbits in planar vector fields and heteroclinic persisting perturbations |
| url | http://dx.doi.org/10.1155/2021/5140694 |
| work_keys_str_mv | AT yizhong ahighordermelnikovmethodforheteroclinicorbitsinplanarvectorfieldsandheteroclinicpersistingperturbations AT yizhong highordermelnikovmethodforheteroclinicorbitsinplanarvectorfieldsandheteroclinicpersistingperturbations |