Perturbation of a Period Annulus with a Unique Two-Saddle Cycle in Higher Order Hamiltonian
In this paper, we study the number of limit cycles emerging from the period annulus by perturbing the Hamiltonian system x˙=y,y˙=x(x2-1)(x2+1)(x2+2). The period annulus has a heteroclinic cycle connecting two hyperbolic saddles as the outer boundary. It is proved that there exist at most 4 and at le...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/5813596 |
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| _version_ | 1832564827603599360 |
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| author | Hongying Zhu Sumin Yang Xiaochun Hu Weihua Huang |
| author_facet | Hongying Zhu Sumin Yang Xiaochun Hu Weihua Huang |
| author_sort | Hongying Zhu |
| collection | DOAJ |
| description | In this paper, we study the number of limit cycles emerging from the period annulus by perturbing the Hamiltonian system x˙=y,y˙=x(x2-1)(x2+1)(x2+2). The period annulus has a heteroclinic cycle connecting two hyperbolic saddles as the outer boundary. It is proved that there exist at most 4 and at least 3 limit cycles emerging from the period annulus, and 3 limit cycles are near the boundaries. |
| format | Article |
| id | doaj-art-79f99012fa204da2a084a03792968fd9 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-79f99012fa204da2a084a03792968fd92025-02-03T01:10:11ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/58135965813596Perturbation of a Period Annulus with a Unique Two-Saddle Cycle in Higher Order HamiltonianHongying Zhu0Sumin Yang1Xiaochun Hu2Weihua Huang3Department of Applied Mathematics, Guangxi University of Finance and Economics, Nanning, 530003 Guangxi, ChinaDepartment of Human Sciences, Guangxi Technological College of Machinery and Electricity, Nanning, 530007 Guangxi, ChinaDepartment of Applied Mathematics, Guangxi University of Finance and Economics, Nanning, 530003 Guangxi, ChinaDepartment of Applied Mathematics, Guangxi University of Finance and Economics, Nanning, 530003 Guangxi, ChinaIn this paper, we study the number of limit cycles emerging from the period annulus by perturbing the Hamiltonian system x˙=y,y˙=x(x2-1)(x2+1)(x2+2). The period annulus has a heteroclinic cycle connecting two hyperbolic saddles as the outer boundary. It is proved that there exist at most 4 and at least 3 limit cycles emerging from the period annulus, and 3 limit cycles are near the boundaries.http://dx.doi.org/10.1155/2019/5813596 |
| spellingShingle | Hongying Zhu Sumin Yang Xiaochun Hu Weihua Huang Perturbation of a Period Annulus with a Unique Two-Saddle Cycle in Higher Order Hamiltonian Complexity |
| title | Perturbation of a Period Annulus with a Unique Two-Saddle Cycle in Higher Order Hamiltonian |
| title_full | Perturbation of a Period Annulus with a Unique Two-Saddle Cycle in Higher Order Hamiltonian |
| title_fullStr | Perturbation of a Period Annulus with a Unique Two-Saddle Cycle in Higher Order Hamiltonian |
| title_full_unstemmed | Perturbation of a Period Annulus with a Unique Two-Saddle Cycle in Higher Order Hamiltonian |
| title_short | Perturbation of a Period Annulus with a Unique Two-Saddle Cycle in Higher Order Hamiltonian |
| title_sort | perturbation of a period annulus with a unique two saddle cycle in higher order hamiltonian |
| url | http://dx.doi.org/10.1155/2019/5813596 |
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