Limit Cycle Bifurcations by Perturbing a Compound Loop with a Cusp and a Nilpotent Saddle
We study the expansions of the first order Melnikov functions for general near-Hamiltonian systems near a compound loop with a cusp and a nilpotent saddle. We also obtain formulas for the first coefficients appearing in the expansions and then establish a bifurcation theorem on the number of limit c...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/819798 |
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| _version_ | 1832551426805465088 |
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| author | Huanhuan Tian Maoan Han |
| author_facet | Huanhuan Tian Maoan Han |
| author_sort | Huanhuan Tian |
| collection | DOAJ |
| description | We study the expansions of the first order Melnikov functions for general near-Hamiltonian systems near a compound loop with a cusp and a nilpotent saddle. We also obtain formulas for the first coefficients appearing in the expansions and then establish a bifurcation theorem on the number of limit cycles. As an application example, we give a lower bound of the maximal number of limit cycles for a polynomial system of Liénard type. |
| format | Article |
| id | doaj-art-c9dbabdaa47045afb3ee25a6fa708b5e |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-c9dbabdaa47045afb3ee25a6fa708b5e2025-02-03T06:01:30ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/819798819798Limit Cycle Bifurcations by Perturbing a Compound Loop with a Cusp and a Nilpotent SaddleHuanhuan Tian0Maoan Han1Department of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaDepartment of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaWe study the expansions of the first order Melnikov functions for general near-Hamiltonian systems near a compound loop with a cusp and a nilpotent saddle. We also obtain formulas for the first coefficients appearing in the expansions and then establish a bifurcation theorem on the number of limit cycles. As an application example, we give a lower bound of the maximal number of limit cycles for a polynomial system of Liénard type.http://dx.doi.org/10.1155/2014/819798 |
| spellingShingle | Huanhuan Tian Maoan Han Limit Cycle Bifurcations by Perturbing a Compound Loop with a Cusp and a Nilpotent Saddle Abstract and Applied Analysis |
| title | Limit Cycle Bifurcations by Perturbing a Compound Loop with a Cusp and a Nilpotent Saddle |
| title_full | Limit Cycle Bifurcations by Perturbing a Compound Loop with a Cusp and a Nilpotent Saddle |
| title_fullStr | Limit Cycle Bifurcations by Perturbing a Compound Loop with a Cusp and a Nilpotent Saddle |
| title_full_unstemmed | Limit Cycle Bifurcations by Perturbing a Compound Loop with a Cusp and a Nilpotent Saddle |
| title_short | Limit Cycle Bifurcations by Perturbing a Compound Loop with a Cusp and a Nilpotent Saddle |
| title_sort | limit cycle bifurcations by perturbing a compound loop with a cusp and a nilpotent saddle |
| url | http://dx.doi.org/10.1155/2014/819798 |
| work_keys_str_mv | AT huanhuantian limitcyclebifurcationsbyperturbingacompoundloopwithacuspandanilpotentsaddle AT maoanhan limitcyclebifurcationsbyperturbingacompoundloopwithacuspandanilpotentsaddle |