Limit Cycle Bifurcations Near a Cuspidal Loop
In this paper, we study limit cycle bifurcation near a cuspidal loop for a general near-Hamiltonian system by using expansions of the first order Melnikov functions. We give a method to compute more coefficients of the expansions to find more limit cycles near the cuspidal loop. As an application ex...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-08-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/9/1425 |
| _version_ | 1797555400333066240 |
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| author | Pan Liu Maoan Han |
| author_facet | Pan Liu Maoan Han |
| author_sort | Pan Liu |
| collection | DOAJ |
| description | In this paper, we study limit cycle bifurcation near a cuspidal loop for a general near-Hamiltonian system by using expansions of the first order Melnikov functions. We give a method to compute more coefficients of the expansions to find more limit cycles near the cuspidal loop. As an application example, we considered a polynomial near-Hamiltonian system and found 12 limit cycles near the cuspidal loop and the center. |
| first_indexed | 2024-03-10T16:46:57Z |
| format | Article |
| id | doaj.art-7f0c3d0cd56247539c8b8fae9055f15d |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T16:46:57Z |
| publishDate | 2020-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-7f0c3d0cd56247539c8b8fae9055f15d2023-11-20T11:31:30ZengMDPI AGSymmetry2073-89942020-08-01129142510.3390/sym12091425Limit Cycle Bifurcations Near a Cuspidal LoopPan Liu0Maoan Han1Department of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaDepartment of Mathematics, Zhejiang Normal University, Jinhua 321004, ChinaIn this paper, we study limit cycle bifurcation near a cuspidal loop for a general near-Hamiltonian system by using expansions of the first order Melnikov functions. We give a method to compute more coefficients of the expansions to find more limit cycles near the cuspidal loop. As an application example, we considered a polynomial near-Hamiltonian system and found 12 limit cycles near the cuspidal loop and the center.https://www.mdpi.com/2073-8994/12/9/1425limit cyclecuspidal loopMelnikov function |
| spellingShingle | Pan Liu Maoan Han Limit Cycle Bifurcations Near a Cuspidal Loop Symmetry limit cycle cuspidal loop Melnikov function |
| title | Limit Cycle Bifurcations Near a Cuspidal Loop |
| title_full | Limit Cycle Bifurcations Near a Cuspidal Loop |
| title_fullStr | Limit Cycle Bifurcations Near a Cuspidal Loop |
| title_full_unstemmed | Limit Cycle Bifurcations Near a Cuspidal Loop |
| title_short | Limit Cycle Bifurcations Near a Cuspidal Loop |
| title_sort | limit cycle bifurcations near a cuspidal loop |
| topic | limit cycle cuspidal loop Melnikov function |
| url | https://www.mdpi.com/2073-8994/12/9/1425 |
| work_keys_str_mv | AT panliu limitcyclebifurcationsnearacuspidalloop AT maoanhan limitcyclebifurcationsnearacuspidalloop |