Zero-Hopf singularity in bidirectional ring network model with delay
Abstract This paper reports a bidirectional ring network model with delay. Zero-Hopf bifurcation is studied by using the center manifold reduction and the normal form method for retarded functional differential equation. We get the versal unfolding of the norm forms at the zero-Hopf singularity and...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
He, Xing [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2014 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media Dordrecht 2014 |
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| Übergeordnetes Werk: |
Enthalten in: Nonlinear dynamics - Springer Netherlands, 1990, 78(2014), 4 vom: 03. Aug., Seite 2605-2616 |
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| Übergeordnetes Werk: |
volume:78 ; year:2014 ; number:4 ; day:03 ; month:08 ; pages:2605-2616 |
| Links: |
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| DOI / URN: |
10.1007/s11071-014-1612-x |
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OLC2051105855 |
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| 520 | |a Abstract This paper reports a bidirectional ring network model with delay. Zero-Hopf bifurcation is studied by using the center manifold reduction and the normal form method for retarded functional differential equation. We get the versal unfolding of the norm forms at the zero-Hopf singularity and show that the model can exhibit pitchfork and Hopf bifurcation. Some numerical simulations are given to support the analytic results, and near the zero-Hopf singularity point, this model displays quasi-periodic, double periodic and multiple periodic trajectory. | ||
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10.1007/s11071-014-1612-x doi (DE-627)OLC2051105855 (DE-He213)s11071-014-1612-x-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn He, Xing verfasserin aut Zero-Hopf singularity in bidirectional ring network model with delay 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2014 Abstract This paper reports a bidirectional ring network model with delay. Zero-Hopf bifurcation is studied by using the center manifold reduction and the normal form method for retarded functional differential equation. We get the versal unfolding of the norm forms at the zero-Hopf singularity and show that the model can exhibit pitchfork and Hopf bifurcation. Some numerical simulations are given to support the analytic results, and near the zero-Hopf singularity point, this model displays quasi-periodic, double periodic and multiple periodic trajectory. Codimension-two bifurcation Zero-Hopf singularity Ring network model Li, Chuandong aut Huang, Tingwen aut Huang, Junjian aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 78(2014), 4 vom: 03. Aug., Seite 2605-2616 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:78 year:2014 number:4 day:03 month:08 pages:2605-2616 https://doi.org/10.1007/s11071-014-1612-x 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 78 2014 4 03 08 2605-2616 |
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10.1007/s11071-014-1612-x doi (DE-627)OLC2051105855 (DE-He213)s11071-014-1612-x-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn He, Xing verfasserin aut Zero-Hopf singularity in bidirectional ring network model with delay 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2014 Abstract This paper reports a bidirectional ring network model with delay. Zero-Hopf bifurcation is studied by using the center manifold reduction and the normal form method for retarded functional differential equation. We get the versal unfolding of the norm forms at the zero-Hopf singularity and show that the model can exhibit pitchfork and Hopf bifurcation. Some numerical simulations are given to support the analytic results, and near the zero-Hopf singularity point, this model displays quasi-periodic, double periodic and multiple periodic trajectory. Codimension-two bifurcation Zero-Hopf singularity Ring network model Li, Chuandong aut Huang, Tingwen aut Huang, Junjian aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 78(2014), 4 vom: 03. Aug., Seite 2605-2616 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:78 year:2014 number:4 day:03 month:08 pages:2605-2616 https://doi.org/10.1007/s11071-014-1612-x 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 78 2014 4 03 08 2605-2616 |
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10.1007/s11071-014-1612-x doi (DE-627)OLC2051105855 (DE-He213)s11071-014-1612-x-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn He, Xing verfasserin aut Zero-Hopf singularity in bidirectional ring network model with delay 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2014 Abstract This paper reports a bidirectional ring network model with delay. Zero-Hopf bifurcation is studied by using the center manifold reduction and the normal form method for retarded functional differential equation. We get the versal unfolding of the norm forms at the zero-Hopf singularity and show that the model can exhibit pitchfork and Hopf bifurcation. Some numerical simulations are given to support the analytic results, and near the zero-Hopf singularity point, this model displays quasi-periodic, double periodic and multiple periodic trajectory. Codimension-two bifurcation Zero-Hopf singularity Ring network model Li, Chuandong aut Huang, Tingwen aut Huang, Junjian aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 78(2014), 4 vom: 03. Aug., Seite 2605-2616 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:78 year:2014 number:4 day:03 month:08 pages:2605-2616 https://doi.org/10.1007/s11071-014-1612-x 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 78 2014 4 03 08 2605-2616 |
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10.1007/s11071-014-1612-x doi (DE-627)OLC2051105855 (DE-He213)s11071-014-1612-x-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn He, Xing verfasserin aut Zero-Hopf singularity in bidirectional ring network model with delay 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2014 Abstract This paper reports a bidirectional ring network model with delay. Zero-Hopf bifurcation is studied by using the center manifold reduction and the normal form method for retarded functional differential equation. We get the versal unfolding of the norm forms at the zero-Hopf singularity and show that the model can exhibit pitchfork and Hopf bifurcation. Some numerical simulations are given to support the analytic results, and near the zero-Hopf singularity point, this model displays quasi-periodic, double periodic and multiple periodic trajectory. Codimension-two bifurcation Zero-Hopf singularity Ring network model Li, Chuandong aut Huang, Tingwen aut Huang, Junjian aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 78(2014), 4 vom: 03. Aug., Seite 2605-2616 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:78 year:2014 number:4 day:03 month:08 pages:2605-2616 https://doi.org/10.1007/s11071-014-1612-x 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 78 2014 4 03 08 2605-2616 |
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Abstract This paper reports a bidirectional ring network model with delay. Zero-Hopf bifurcation is studied by using the center manifold reduction and the normal form method for retarded functional differential equation. We get the versal unfolding of the norm forms at the zero-Hopf singularity and show that the model can exhibit pitchfork and Hopf bifurcation. Some numerical simulations are given to support the analytic results, and near the zero-Hopf singularity point, this model displays quasi-periodic, double periodic and multiple periodic trajectory. © Springer Science+Business Media Dordrecht 2014 |
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Abstract This paper reports a bidirectional ring network model with delay. Zero-Hopf bifurcation is studied by using the center manifold reduction and the normal form method for retarded functional differential equation. We get the versal unfolding of the norm forms at the zero-Hopf singularity and show that the model can exhibit pitchfork and Hopf bifurcation. Some numerical simulations are given to support the analytic results, and near the zero-Hopf singularity point, this model displays quasi-periodic, double periodic and multiple periodic trajectory. © Springer Science+Business Media Dordrecht 2014 |
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Abstract This paper reports a bidirectional ring network model with delay. Zero-Hopf bifurcation is studied by using the center manifold reduction and the normal form method for retarded functional differential equation. We get the versal unfolding of the norm forms at the zero-Hopf singularity and show that the model can exhibit pitchfork and Hopf bifurcation. Some numerical simulations are given to support the analytic results, and near the zero-Hopf singularity point, this model displays quasi-periodic, double periodic and multiple periodic trajectory. © Springer Science+Business Media Dordrecht 2014 |
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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">OLC2051105855</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230503230424.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200820s2014 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s11071-014-1612-x</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2051105855</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s11071-014-1612-x-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">He, Xing</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Zero-Hopf singularity in bidirectional ring network model with delay</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2014</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 2014</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract This paper reports a bidirectional ring network model with delay. Zero-Hopf bifurcation is studied by using the center manifold reduction and the normal form method for retarded functional differential equation. We get the versal unfolding of the norm forms at the zero-Hopf singularity and show that the model can exhibit pitchfork and Hopf bifurcation. Some numerical simulations are given to support the analytic results, and near the zero-Hopf singularity point, this model displays quasi-periodic, double periodic and multiple periodic trajectory.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Codimension-two bifurcation</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Zero-Hopf singularity</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Ring network model</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Li, Chuandong</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Huang, Tingwen</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Huang, Junjian</subfield><subfield code="4">aut</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">78(2014), 4 vom: 03. Aug., Seite 2605-2616</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:78</subfield><subfield code="g">year:2014</subfield><subfield code="g">number:4</subfield><subfield code="g">day:03</subfield><subfield code="g">month:08</subfield><subfield code="g">pages:2605-2616</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s11071-014-1612-x</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">78</subfield><subfield code="j">2014</subfield><subfield code="e">4</subfield><subfield code="b">03</subfield><subfield code="c">08</subfield><subfield code="h">2605-2616</subfield></datafield></record></collection>
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