Limit Cycles and Integrability in a Class of Systems with High-Order Nilpotent Critical Points
A class of polynomial differential systems with high-order nilpotent critical points are investigated in this paper. Those systems could be changed into systems with an element critical point. The center conditions and bifurcation of limit cycles could be obtained by classical methods. Finally, an e...
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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/10.1155/2013/861052 |
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| _version_ | 1849412911287500800 |
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| author | Feng Li Jianlong Qiu |
| author_facet | Feng Li Jianlong Qiu |
| author_sort | Feng Li |
| collection | DOAJ |
| description | A class of polynomial differential systems with high-order nilpotent critical points are investigated in this paper. Those systems could be changed into systems with an element critical point. The center conditions and bifurcation of limit cycles could be obtained by classical methods. Finally, an example was given; with the help of computer algebra system MATHEMATICA, the first 5 Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there exist 5 small amplitude limit cycles created from the high-order nilpotent critical point is also proved. |
| format | Article |
| id | doaj-art-4c9f6db6b2924b49a56cafeed074a3fa |
| 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-4c9f6db6b2924b49a56cafeed074a3fa2025-08-20T03:34:18ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/861052861052Limit Cycles and Integrability in a Class of Systems with High-Order Nilpotent Critical PointsFeng Li0Jianlong Qiu1School of Science, Linyi University, Shandong, Linyi 276005, ChinaSchool of Science, Linyi University, Shandong, Linyi 276005, ChinaA class of polynomial differential systems with high-order nilpotent critical points are investigated in this paper. Those systems could be changed into systems with an element critical point. The center conditions and bifurcation of limit cycles could be obtained by classical methods. Finally, an example was given; with the help of computer algebra system MATHEMATICA, the first 5 Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there exist 5 small amplitude limit cycles created from the high-order nilpotent critical point is also proved.http://dx.doi.org/10.1155/2013/861052 |
| spellingShingle | Feng Li Jianlong Qiu Limit Cycles and Integrability in a Class of Systems with High-Order Nilpotent Critical Points Abstract and Applied Analysis |
| title | Limit Cycles and Integrability in a Class of Systems with High-Order Nilpotent Critical Points |
| title_full | Limit Cycles and Integrability in a Class of Systems with High-Order Nilpotent Critical Points |
| title_fullStr | Limit Cycles and Integrability in a Class of Systems with High-Order Nilpotent Critical Points |
| title_full_unstemmed | Limit Cycles and Integrability in a Class of Systems with High-Order Nilpotent Critical Points |
| title_short | Limit Cycles and Integrability in a Class of Systems with High-Order Nilpotent Critical Points |
| title_sort | limit cycles and integrability in a class of systems with high order nilpotent critical points |
| url | http://dx.doi.org/10.1155/2013/861052 |
| work_keys_str_mv | AT fengli limitcyclesandintegrabilityinaclassofsystemswithhighordernilpotentcriticalpoints AT jianlongqiu limitcyclesandintegrabilityinaclassofsystemswithhighordernilpotentcriticalpoints |