A degenerate Hopf–saddle-node bifurcation analysis in a family of electronic circuits
Abstract This paper presents a study of a three-parameter unfolding of a degenerate case in the Hopf--saddle-node singularity. This analysis shows that this nonlinear degeneracy is a source of interesting bifurcations of periodic orbits as well as global bifurcations of equilibria. The results achie...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Algaba, A. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2006 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media, Inc. 2006 |
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| Übergeordnetes Werk: |
Enthalten in: Nonlinear dynamics - Kluwer Academic Publishers, 1990, 48(2006), 1-2 vom: 29. Nov., Seite 55-76 |
|---|---|
| Übergeordnetes Werk: |
volume:48 ; year:2006 ; number:1-2 ; day:29 ; month:11 ; pages:55-76 |
| Links: |
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| DOI / URN: |
10.1007/s11071-006-9051-y |
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OLC2051081956 |
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| 520 | |a Abstract This paper presents a study of a three-parameter unfolding of a degenerate case in the Hopf--saddle-node singularity. This analysis shows that this nonlinear degeneracy is a source of interesting bifurcations of periodic orbits as well as global bifurcations of equilibria. The results achieved are applied to the study of a simple autonomous electronic circuit, which has just only one nonlinearity. The numerical results include the analysis of interesting resonance behaviors. | ||
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10.1007/s11071-006-9051-y doi (DE-627)OLC2051081956 (DE-He213)s11071-006-9051-y-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Algaba, A. verfasserin aut A degenerate Hopf–saddle-node bifurcation analysis in a family of electronic circuits 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, Inc. 2006 Abstract This paper presents a study of a three-parameter unfolding of a degenerate case in the Hopf--saddle-node singularity. This analysis shows that this nonlinear degeneracy is a source of interesting bifurcations of periodic orbits as well as global bifurcations of equilibria. The results achieved are applied to the study of a simple autonomous electronic circuit, which has just only one nonlinearity. The numerical results include the analysis of interesting resonance behaviors. Bifurcations Hopf–saddle-node Resonances Invariant torus Gamero, E. aut García, C. aut Merino, M. aut Enthalten in Nonlinear dynamics Kluwer Academic Publishers, 1990 48(2006), 1-2 vom: 29. Nov., Seite 55-76 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:48 year:2006 number:1-2 day:29 month:11 pages:55-76 https://doi.org/10.1007/s11071-006-9051-y 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_23 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_4307 AR 48 2006 1-2 29 11 55-76 |
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10.1007/s11071-006-9051-y doi (DE-627)OLC2051081956 (DE-He213)s11071-006-9051-y-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Algaba, A. verfasserin aut A degenerate Hopf–saddle-node bifurcation analysis in a family of electronic circuits 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, Inc. 2006 Abstract This paper presents a study of a three-parameter unfolding of a degenerate case in the Hopf--saddle-node singularity. This analysis shows that this nonlinear degeneracy is a source of interesting bifurcations of periodic orbits as well as global bifurcations of equilibria. The results achieved are applied to the study of a simple autonomous electronic circuit, which has just only one nonlinearity. The numerical results include the analysis of interesting resonance behaviors. Bifurcations Hopf–saddle-node Resonances Invariant torus Gamero, E. aut García, C. aut Merino, M. aut Enthalten in Nonlinear dynamics Kluwer Academic Publishers, 1990 48(2006), 1-2 vom: 29. Nov., Seite 55-76 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:48 year:2006 number:1-2 day:29 month:11 pages:55-76 https://doi.org/10.1007/s11071-006-9051-y 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_23 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_4307 AR 48 2006 1-2 29 11 55-76 |
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10.1007/s11071-006-9051-y doi (DE-627)OLC2051081956 (DE-He213)s11071-006-9051-y-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Algaba, A. verfasserin aut A degenerate Hopf–saddle-node bifurcation analysis in a family of electronic circuits 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, Inc. 2006 Abstract This paper presents a study of a three-parameter unfolding of a degenerate case in the Hopf--saddle-node singularity. This analysis shows that this nonlinear degeneracy is a source of interesting bifurcations of periodic orbits as well as global bifurcations of equilibria. The results achieved are applied to the study of a simple autonomous electronic circuit, which has just only one nonlinearity. The numerical results include the analysis of interesting resonance behaviors. Bifurcations Hopf–saddle-node Resonances Invariant torus Gamero, E. aut García, C. aut Merino, M. aut Enthalten in Nonlinear dynamics Kluwer Academic Publishers, 1990 48(2006), 1-2 vom: 29. Nov., Seite 55-76 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:48 year:2006 number:1-2 day:29 month:11 pages:55-76 https://doi.org/10.1007/s11071-006-9051-y 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_23 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_4307 AR 48 2006 1-2 29 11 55-76 |
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10.1007/s11071-006-9051-y doi (DE-627)OLC2051081956 (DE-He213)s11071-006-9051-y-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Algaba, A. verfasserin aut A degenerate Hopf–saddle-node bifurcation analysis in a family of electronic circuits 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, Inc. 2006 Abstract This paper presents a study of a three-parameter unfolding of a degenerate case in the Hopf--saddle-node singularity. This analysis shows that this nonlinear degeneracy is a source of interesting bifurcations of periodic orbits as well as global bifurcations of equilibria. The results achieved are applied to the study of a simple autonomous electronic circuit, which has just only one nonlinearity. The numerical results include the analysis of interesting resonance behaviors. Bifurcations Hopf–saddle-node Resonances Invariant torus Gamero, E. aut García, C. aut Merino, M. aut Enthalten in Nonlinear dynamics Kluwer Academic Publishers, 1990 48(2006), 1-2 vom: 29. Nov., Seite 55-76 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:48 year:2006 number:1-2 day:29 month:11 pages:55-76 https://doi.org/10.1007/s11071-006-9051-y 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_23 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_4307 AR 48 2006 1-2 29 11 55-76 |
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10.1007/s11071-006-9051-y doi (DE-627)OLC2051081956 (DE-He213)s11071-006-9051-y-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Algaba, A. verfasserin aut A degenerate Hopf–saddle-node bifurcation analysis in a family of electronic circuits 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, Inc. 2006 Abstract This paper presents a study of a three-parameter unfolding of a degenerate case in the Hopf--saddle-node singularity. This analysis shows that this nonlinear degeneracy is a source of interesting bifurcations of periodic orbits as well as global bifurcations of equilibria. The results achieved are applied to the study of a simple autonomous electronic circuit, which has just only one nonlinearity. The numerical results include the analysis of interesting resonance behaviors. Bifurcations Hopf–saddle-node Resonances Invariant torus Gamero, E. aut García, C. aut Merino, M. aut Enthalten in Nonlinear dynamics Kluwer Academic Publishers, 1990 48(2006), 1-2 vom: 29. Nov., Seite 55-76 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:48 year:2006 number:1-2 day:29 month:11 pages:55-76 https://doi.org/10.1007/s11071-006-9051-y 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_23 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2006 GBV_ILN_4307 AR 48 2006 1-2 29 11 55-76 |
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Abstract This paper presents a study of a three-parameter unfolding of a degenerate case in the Hopf--saddle-node singularity. This analysis shows that this nonlinear degeneracy is a source of interesting bifurcations of periodic orbits as well as global bifurcations of equilibria. The results achieved are applied to the study of a simple autonomous electronic circuit, which has just only one nonlinearity. The numerical results include the analysis of interesting resonance behaviors. © Springer Science+Business Media, Inc. 2006 |
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Abstract This paper presents a study of a three-parameter unfolding of a degenerate case in the Hopf--saddle-node singularity. This analysis shows that this nonlinear degeneracy is a source of interesting bifurcations of periodic orbits as well as global bifurcations of equilibria. The results achieved are applied to the study of a simple autonomous electronic circuit, which has just only one nonlinearity. The numerical results include the analysis of interesting resonance behaviors. © Springer Science+Business Media, Inc. 2006 |
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Abstract This paper presents a study of a three-parameter unfolding of a degenerate case in the Hopf--saddle-node singularity. This analysis shows that this nonlinear degeneracy is a source of interesting bifurcations of periodic orbits as well as global bifurcations of equilibria. The results achieved are applied to the study of a simple autonomous electronic circuit, which has just only one nonlinearity. The numerical results include the analysis of interesting resonance behaviors. © Springer Science+Business Media, Inc. 2006 |
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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">OLC2051081956</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230503224513.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200820s2006 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s11071-006-9051-y</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2051081956</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s11071-006-9051-y-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">Algaba, A.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">A degenerate Hopf–saddle-node bifurcation analysis in a family of electronic circuits</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2006</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, Inc. 2006</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract This paper presents a study of a three-parameter unfolding of a degenerate case in the Hopf--saddle-node singularity. This analysis shows that this nonlinear degeneracy is a source of interesting bifurcations of periodic orbits as well as global bifurcations of equilibria. The results achieved are applied to the study of a simple autonomous electronic circuit, which has just only one nonlinearity. The numerical results include the analysis of interesting resonance behaviors.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Bifurcations</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Hopf–saddle-node</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Resonances</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Invariant torus</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Gamero, E.</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">García, C.</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Merino, M.</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">Kluwer Academic Publishers, 1990</subfield><subfield code="g">48(2006), 1-2 vom: 29. 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