Poincaré Bifurcation of Limit Cycles from a Liénard System with a Homoclinic Loop Passing through a Nilpotent Saddle
In present paper, the number of zeros of the Abelian integral is studied, which is for some perturbed Hamiltonian system of degree 6. We prove the generating elements of the Abelian integral from a Chebyshev system of accuracy of 3; therefore there are at most 6 zeros of the Abelian integral.
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2019/6943563 |
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| _version_ | 1849405008222617600 |
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| author | Minzhi Wei Junning Cai Hongying Zhu |
| author_facet | Minzhi Wei Junning Cai Hongying Zhu |
| author_sort | Minzhi Wei |
| collection | DOAJ |
| description | In present paper, the number of zeros of the Abelian integral is studied, which is for some perturbed Hamiltonian system of degree 6. We prove the generating elements of the Abelian integral from a Chebyshev system of accuracy of 3; therefore there are at most 6 zeros of the Abelian integral. |
| format | Article |
| id | doaj-art-491ce89c35b74cafba9288c8d1fbcb63 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-491ce89c35b74cafba9288c8d1fbcb632025-08-20T03:36:47ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2019-01-01201910.1155/2019/69435636943563Poincaré Bifurcation of Limit Cycles from a Liénard System with a Homoclinic Loop Passing through a Nilpotent SaddleMinzhi Wei0Junning Cai1Hongying Zhu2Department of Applied Mathematics, Guangxi University of Finance and Economics, Nanning, Guangxi, 530003, ChinaDepartment of Applied Mathematics, Guangxi University of Finance and Economics, Nanning, Guangxi, 530003, ChinaDepartment of Applied Mathematics, Guangxi University of Finance and Economics, Nanning, Guangxi, 530003, ChinaIn present paper, the number of zeros of the Abelian integral is studied, which is for some perturbed Hamiltonian system of degree 6. We prove the generating elements of the Abelian integral from a Chebyshev system of accuracy of 3; therefore there are at most 6 zeros of the Abelian integral.http://dx.doi.org/10.1155/2019/6943563 |
| spellingShingle | Minzhi Wei Junning Cai Hongying Zhu Poincaré Bifurcation of Limit Cycles from a Liénard System with a Homoclinic Loop Passing through a Nilpotent Saddle Discrete Dynamics in Nature and Society |
| title | Poincaré Bifurcation of Limit Cycles from a Liénard System with a Homoclinic Loop Passing through a Nilpotent Saddle |
| title_full | Poincaré Bifurcation of Limit Cycles from a Liénard System with a Homoclinic Loop Passing through a Nilpotent Saddle |
| title_fullStr | Poincaré Bifurcation of Limit Cycles from a Liénard System with a Homoclinic Loop Passing through a Nilpotent Saddle |
| title_full_unstemmed | Poincaré Bifurcation of Limit Cycles from a Liénard System with a Homoclinic Loop Passing through a Nilpotent Saddle |
| title_short | Poincaré Bifurcation of Limit Cycles from a Liénard System with a Homoclinic Loop Passing through a Nilpotent Saddle |
| title_sort | poincare bifurcation of limit cycles from a lienard system with a homoclinic loop passing through a nilpotent saddle |
| url | http://dx.doi.org/10.1155/2019/6943563 |
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