Limit cycles and integrability in a class of system with a high-order critical point
Abstract In this paper, a class of polynomial differential system with high-order critical point are investigated. The system could be changed into a system with a 3-order nilpotent critical point. Finally, an example was given, with the help of computer algebra system MATHEMATICA, the first three q...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Feng, Li [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2013 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media Dordrecht 2013 |
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| Übergeordnetes Werk: |
Enthalten in: Nonlinear dynamics - Springer Netherlands, 1990, 73(2013), 1-2 vom: 02. März, Seite 665-670 |
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| Übergeordnetes Werk: |
volume:73 ; year:2013 ; number:1-2 ; day:02 ; month:03 ; pages:665-670 |
| Links: |
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| DOI / URN: |
10.1007/s11071-013-0820-0 |
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OLC2051097747 |
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| 520 | |a Abstract In this paper, a class of polynomial differential system with high-order critical point are investigated. The system could be changed into a system with a 3-order nilpotent critical point. Finally, an example was given, with the help of computer algebra system MATHEMATICA, the first three quasi-Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there three small amplitude limit cycles created from the 3-order nilpotent critical point is also proved. | ||
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10.1007/s11071-013-0820-0 doi (DE-627)OLC2051097747 (DE-He213)s11071-013-0820-0-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Feng, Li verfasserin aut Limit cycles and integrability in a class of system with a high-order critical point 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2013 Abstract In this paper, a class of polynomial differential system with high-order critical point are investigated. The system could be changed into a system with a 3-order nilpotent critical point. Finally, an example was given, with the help of computer algebra system MATHEMATICA, the first three quasi-Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there three small amplitude limit cycles created from the 3-order nilpotent critical point is also proved. High-order critical point Nilpotent critical point Center Focus Bifurcation of limit cycle Enthalten in Nonlinear dynamics Springer Netherlands, 1990 73(2013), 1-2 vom: 02. März, Seite 665-670 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:73 year:2013 number:1-2 day:02 month:03 pages:665-670 https://doi.org/10.1007/s11071-013-0820-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 73 2013 1-2 02 03 665-670 |
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10.1007/s11071-013-0820-0 doi (DE-627)OLC2051097747 (DE-He213)s11071-013-0820-0-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Feng, Li verfasserin aut Limit cycles and integrability in a class of system with a high-order critical point 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2013 Abstract In this paper, a class of polynomial differential system with high-order critical point are investigated. The system could be changed into a system with a 3-order nilpotent critical point. Finally, an example was given, with the help of computer algebra system MATHEMATICA, the first three quasi-Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there three small amplitude limit cycles created from the 3-order nilpotent critical point is also proved. High-order critical point Nilpotent critical point Center Focus Bifurcation of limit cycle Enthalten in Nonlinear dynamics Springer Netherlands, 1990 73(2013), 1-2 vom: 02. März, Seite 665-670 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:73 year:2013 number:1-2 day:02 month:03 pages:665-670 https://doi.org/10.1007/s11071-013-0820-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 73 2013 1-2 02 03 665-670 |
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10.1007/s11071-013-0820-0 doi (DE-627)OLC2051097747 (DE-He213)s11071-013-0820-0-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Feng, Li verfasserin aut Limit cycles and integrability in a class of system with a high-order critical point 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2013 Abstract In this paper, a class of polynomial differential system with high-order critical point are investigated. The system could be changed into a system with a 3-order nilpotent critical point. Finally, an example was given, with the help of computer algebra system MATHEMATICA, the first three quasi-Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there three small amplitude limit cycles created from the 3-order nilpotent critical point is also proved. High-order critical point Nilpotent critical point Center Focus Bifurcation of limit cycle Enthalten in Nonlinear dynamics Springer Netherlands, 1990 73(2013), 1-2 vom: 02. März, Seite 665-670 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:73 year:2013 number:1-2 day:02 month:03 pages:665-670 https://doi.org/10.1007/s11071-013-0820-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 73 2013 1-2 02 03 665-670 |
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10.1007/s11071-013-0820-0 doi (DE-627)OLC2051097747 (DE-He213)s11071-013-0820-0-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Feng, Li verfasserin aut Limit cycles and integrability in a class of system with a high-order critical point 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2013 Abstract In this paper, a class of polynomial differential system with high-order critical point are investigated. The system could be changed into a system with a 3-order nilpotent critical point. Finally, an example was given, with the help of computer algebra system MATHEMATICA, the first three quasi-Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there three small amplitude limit cycles created from the 3-order nilpotent critical point is also proved. High-order critical point Nilpotent critical point Center Focus Bifurcation of limit cycle Enthalten in Nonlinear dynamics Springer Netherlands, 1990 73(2013), 1-2 vom: 02. März, Seite 665-670 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:73 year:2013 number:1-2 day:02 month:03 pages:665-670 https://doi.org/10.1007/s11071-013-0820-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-CHE SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 73 2013 1-2 02 03 665-670 |
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Abstract In this paper, a class of polynomial differential system with high-order critical point are investigated. The system could be changed into a system with a 3-order nilpotent critical point. Finally, an example was given, with the help of computer algebra system MATHEMATICA, the first three quasi-Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there three small amplitude limit cycles created from the 3-order nilpotent critical point is also proved. © Springer Science+Business Media Dordrecht 2013 |
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Abstract In this paper, a class of polynomial differential system with high-order critical point are investigated. The system could be changed into a system with a 3-order nilpotent critical point. Finally, an example was given, with the help of computer algebra system MATHEMATICA, the first three quasi-Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there three small amplitude limit cycles created from the 3-order nilpotent critical point is also proved. © Springer Science+Business Media Dordrecht 2013 |
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Abstract In this paper, a class of polynomial differential system with high-order critical point are investigated. The system could be changed into a system with a 3-order nilpotent critical point. Finally, an example was given, with the help of computer algebra system MATHEMATICA, the first three quasi-Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there three small amplitude limit cycles created from the 3-order nilpotent critical point is also proved. © Springer Science+Business Media Dordrecht 2013 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2051097747</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230503225818.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200820s2013 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s11071-013-0820-0</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2051097747</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s11071-013-0820-0-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">11</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Feng, Li</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Limit cycles and integrability in a class of system with a high-order critical point</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2013</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer Science+Business Media Dordrecht 2013</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In this paper, a class of polynomial differential system with high-order critical point are investigated. The system could be changed into a system with a 3-order nilpotent critical point. Finally, an example was given, with the help of computer algebra system MATHEMATICA, the first three quasi-Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there three small amplitude limit cycles created from the 3-order nilpotent critical point is also proved.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">High-order critical point</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Nilpotent critical point</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Center</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Focus</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Bifurcation of limit cycle</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Nonlinear dynamics</subfield><subfield code="d">Springer Netherlands, 1990</subfield><subfield code="g">73(2013), 1-2 vom: 02. März, Seite 665-670</subfield><subfield code="w">(DE-627)130936782</subfield><subfield code="w">(DE-600)1058624-6</subfield><subfield code="w">(DE-576)034188126</subfield><subfield code="x">0924-090X</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:73</subfield><subfield code="g">year:2013</subfield><subfield code="g">number:1-2</subfield><subfield code="g">day:02</subfield><subfield code="g">month:03</subfield><subfield code="g">pages:665-670</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s11071-013-0820-0</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-TEC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-CHE</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OPC-MAT</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">73</subfield><subfield code="j">2013</subfield><subfield code="e">1-2</subfield><subfield code="b">02</subfield><subfield code="c">03</subfield><subfield code="h">665-670</subfield></datafield></record></collection>
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