Bifurcation of Limit Cycles by Perturbing a Piecewise Linear Hamiltonian System
This paper concerns limit cycle bifurcations by perturbing a piecewise linear Hamiltonian system. We first obtain all phase portraits of the unperturbed system having at least one family of periodic orbits. By using the first-order Melnikov function of the piecewise near-Hamiltonian system, we inves...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/575390 |
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| _version_ | 1832567118331117568 |
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| author | Yanqin Xiong Maoan Han |
| author_facet | Yanqin Xiong Maoan Han |
| author_sort | Yanqin Xiong |
| collection | DOAJ |
| description | This paper concerns limit cycle bifurcations by perturbing a piecewise linear Hamiltonian system. We first obtain all phase portraits of the unperturbed system having at least one family of periodic orbits. By using the first-order Melnikov function of the piecewise near-Hamiltonian system, we investigate the maximal number of limit cycles that bifurcate from a global center up to first order of ε. |
| format | Article |
| id | doaj-art-a2d4c4b1747143e187b7e9f07dddf97a |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-a2d4c4b1747143e187b7e9f07dddf97a2025-02-03T01:02:25ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/575390575390Bifurcation of Limit Cycles by Perturbing a Piecewise Linear Hamiltonian SystemYanqin Xiong0Maoan Han1Department of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaDepartment of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaThis paper concerns limit cycle bifurcations by perturbing a piecewise linear Hamiltonian system. We first obtain all phase portraits of the unperturbed system having at least one family of periodic orbits. By using the first-order Melnikov function of the piecewise near-Hamiltonian system, we investigate the maximal number of limit cycles that bifurcate from a global center up to first order of ε.http://dx.doi.org/10.1155/2013/575390 |
| spellingShingle | Yanqin Xiong Maoan Han Bifurcation of Limit Cycles by Perturbing a Piecewise Linear Hamiltonian System Abstract and Applied Analysis |
| title | Bifurcation of Limit Cycles by Perturbing a Piecewise Linear Hamiltonian System |
| title_full | Bifurcation of Limit Cycles by Perturbing a Piecewise Linear Hamiltonian System |
| title_fullStr | Bifurcation of Limit Cycles by Perturbing a Piecewise Linear Hamiltonian System |
| title_full_unstemmed | Bifurcation of Limit Cycles by Perturbing a Piecewise Linear Hamiltonian System |
| title_short | Bifurcation of Limit Cycles by Perturbing a Piecewise Linear Hamiltonian System |
| title_sort | bifurcation of limit cycles by perturbing a piecewise linear hamiltonian system |
| url | http://dx.doi.org/10.1155/2013/575390 |
| work_keys_str_mv | AT yanqinxiong bifurcationoflimitcyclesbyperturbingapiecewiselinearhamiltoniansystem AT maoanhan bifurcationoflimitcyclesbyperturbingapiecewiselinearhamiltoniansystem |