Global bifurcations of strongly nonlinear oscillator induced by parametric and external excitation

Abstract The global bifurcation of strongly nonlinear oscillator induced by parametric and external excitation is researched. It is known that the parametric and external excitation may induce additional saddle states, and result in chaos in the phase space, which cannot be detected by applying the...
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Autor*in:	Wang, Wei [verfasserIn] Zhang, QiChang [verfasserIn] Feng, JingJing [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2011

Schlagwörter:	global bifurcation strongly nonlinear chaos Melnikov method

Übergeordnetes Werk:	Enthalten in: Science in China - Heidelberg : Springer, 1997, 54(2011), 8 vom: 24. Juni, Seite 1986-1991
Übergeordnetes Werk:	volume:54 ; year:2011 ; number:8 ; day:24 ; month:06 ; pages:1986-1991

Links:	Volltext

DOI / URN:	10.1007/s11431-011-4471-4

Katalog-ID:	SPR019271859

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520			\|a Abstract The global bifurcation of strongly nonlinear oscillator induced by parametric and external excitation is researched. It is known that the parametric and external excitation may induce additional saddle states, and result in chaos in the phase space, which cannot be detected by applying the Melnikov method directly. A feasible solution for this problem is the combination of the averaged equations and Melnikov method. Therefore, we consider the averaged equations of the system subject to Duffing-Van der Pol strong nonlinearity by introducing the undetermined fundamental frequency. Then the bifurcation values of homoclinic structure formation are detected through the combined application of the new averaged equations with Melnikov integration. Finally, the explicit application shows the analytical conditions coincide with the results of numerical simulation even disturbing parameter is of arbitrary magnitude.
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allfields	10.1007/s11431-011-4471-4 doi (DE-627)SPR019271859 (SPR)s11431-011-4471-4-e DE-627 ger DE-627 rakwb eng 600 ASE 600 ASE 50.00 bkl Wang, Wei verfasserin aut Global bifurcations of strongly nonlinear oscillator induced by parametric and external excitation 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The global bifurcation of strongly nonlinear oscillator induced by parametric and external excitation is researched. It is known that the parametric and external excitation may induce additional saddle states, and result in chaos in the phase space, which cannot be detected by applying the Melnikov method directly. A feasible solution for this problem is the combination of the averaged equations and Melnikov method. Therefore, we consider the averaged equations of the system subject to Duffing-Van der Pol strong nonlinearity by introducing the undetermined fundamental frequency. Then the bifurcation values of homoclinic structure formation are detected through the combined application of the new averaged equations with Melnikov integration. Finally, the explicit application shows the analytical conditions coincide with the results of numerical simulation even disturbing parameter is of arbitrary magnitude. global bifurcation (dpeaa)DE-He213 strongly nonlinear (dpeaa)DE-He213 chaos (dpeaa)DE-He213 Melnikov method (dpeaa)DE-He213 Zhang, QiChang verfasserin aut Feng, JingJing verfasserin aut Enthalten in Science in China Heidelberg : Springer, 1997 54(2011), 8 vom: 24. Juni, Seite 1986-1991 (DE-627)385614756 (DE-600)2142897-9 1862-281X nnns volume:54 year:2011 number:8 day:24 month:06 pages:1986-1991 https://dx.doi.org/10.1007/s11431-011-4471-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 50.00 ASE AR 54 2011 8 24 06 1986-1991
spelling	10.1007/s11431-011-4471-4 doi (DE-627)SPR019271859 (SPR)s11431-011-4471-4-e DE-627 ger DE-627 rakwb eng 600 ASE 600 ASE 50.00 bkl Wang, Wei verfasserin aut Global bifurcations of strongly nonlinear oscillator induced by parametric and external excitation 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The global bifurcation of strongly nonlinear oscillator induced by parametric and external excitation is researched. It is known that the parametric and external excitation may induce additional saddle states, and result in chaos in the phase space, which cannot be detected by applying the Melnikov method directly. A feasible solution for this problem is the combination of the averaged equations and Melnikov method. Therefore, we consider the averaged equations of the system subject to Duffing-Van der Pol strong nonlinearity by introducing the undetermined fundamental frequency. Then the bifurcation values of homoclinic structure formation are detected through the combined application of the new averaged equations with Melnikov integration. Finally, the explicit application shows the analytical conditions coincide with the results of numerical simulation even disturbing parameter is of arbitrary magnitude. global bifurcation (dpeaa)DE-He213 strongly nonlinear (dpeaa)DE-He213 chaos (dpeaa)DE-He213 Melnikov method (dpeaa)DE-He213 Zhang, QiChang verfasserin aut Feng, JingJing verfasserin aut Enthalten in Science in China Heidelberg : Springer, 1997 54(2011), 8 vom: 24. Juni, Seite 1986-1991 (DE-627)385614756 (DE-600)2142897-9 1862-281X nnns volume:54 year:2011 number:8 day:24 month:06 pages:1986-1991 https://dx.doi.org/10.1007/s11431-011-4471-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 50.00 ASE AR 54 2011 8 24 06 1986-1991
allfields_unstemmed	10.1007/s11431-011-4471-4 doi (DE-627)SPR019271859 (SPR)s11431-011-4471-4-e DE-627 ger DE-627 rakwb eng 600 ASE 600 ASE 50.00 bkl Wang, Wei verfasserin aut Global bifurcations of strongly nonlinear oscillator induced by parametric and external excitation 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The global bifurcation of strongly nonlinear oscillator induced by parametric and external excitation is researched. It is known that the parametric and external excitation may induce additional saddle states, and result in chaos in the phase space, which cannot be detected by applying the Melnikov method directly. A feasible solution for this problem is the combination of the averaged equations and Melnikov method. Therefore, we consider the averaged equations of the system subject to Duffing-Van der Pol strong nonlinearity by introducing the undetermined fundamental frequency. Then the bifurcation values of homoclinic structure formation are detected through the combined application of the new averaged equations with Melnikov integration. Finally, the explicit application shows the analytical conditions coincide with the results of numerical simulation even disturbing parameter is of arbitrary magnitude. global bifurcation (dpeaa)DE-He213 strongly nonlinear (dpeaa)DE-He213 chaos (dpeaa)DE-He213 Melnikov method (dpeaa)DE-He213 Zhang, QiChang verfasserin aut Feng, JingJing verfasserin aut Enthalten in Science in China Heidelberg : Springer, 1997 54(2011), 8 vom: 24. Juni, Seite 1986-1991 (DE-627)385614756 (DE-600)2142897-9 1862-281X nnns volume:54 year:2011 number:8 day:24 month:06 pages:1986-1991 https://dx.doi.org/10.1007/s11431-011-4471-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 50.00 ASE AR 54 2011 8 24 06 1986-1991
allfieldsGer	10.1007/s11431-011-4471-4 doi (DE-627)SPR019271859 (SPR)s11431-011-4471-4-e DE-627 ger DE-627 rakwb eng 600 ASE 600 ASE 50.00 bkl Wang, Wei verfasserin aut Global bifurcations of strongly nonlinear oscillator induced by parametric and external excitation 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The global bifurcation of strongly nonlinear oscillator induced by parametric and external excitation is researched. It is known that the parametric and external excitation may induce additional saddle states, and result in chaos in the phase space, which cannot be detected by applying the Melnikov method directly. A feasible solution for this problem is the combination of the averaged equations and Melnikov method. Therefore, we consider the averaged equations of the system subject to Duffing-Van der Pol strong nonlinearity by introducing the undetermined fundamental frequency. Then the bifurcation values of homoclinic structure formation are detected through the combined application of the new averaged equations with Melnikov integration. Finally, the explicit application shows the analytical conditions coincide with the results of numerical simulation even disturbing parameter is of arbitrary magnitude. global bifurcation (dpeaa)DE-He213 strongly nonlinear (dpeaa)DE-He213 chaos (dpeaa)DE-He213 Melnikov method (dpeaa)DE-He213 Zhang, QiChang verfasserin aut Feng, JingJing verfasserin aut Enthalten in Science in China Heidelberg : Springer, 1997 54(2011), 8 vom: 24. Juni, Seite 1986-1991 (DE-627)385614756 (DE-600)2142897-9 1862-281X nnns volume:54 year:2011 number:8 day:24 month:06 pages:1986-1991 https://dx.doi.org/10.1007/s11431-011-4471-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 50.00 ASE AR 54 2011 8 24 06 1986-1991
allfieldsSound	10.1007/s11431-011-4471-4 doi (DE-627)SPR019271859 (SPR)s11431-011-4471-4-e DE-627 ger DE-627 rakwb eng 600 ASE 600 ASE 50.00 bkl Wang, Wei verfasserin aut Global bifurcations of strongly nonlinear oscillator induced by parametric and external excitation 2011 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract The global bifurcation of strongly nonlinear oscillator induced by parametric and external excitation is researched. It is known that the parametric and external excitation may induce additional saddle states, and result in chaos in the phase space, which cannot be detected by applying the Melnikov method directly. A feasible solution for this problem is the combination of the averaged equations and Melnikov method. Therefore, we consider the averaged equations of the system subject to Duffing-Van der Pol strong nonlinearity by introducing the undetermined fundamental frequency. Then the bifurcation values of homoclinic structure formation are detected through the combined application of the new averaged equations with Melnikov integration. Finally, the explicit application shows the analytical conditions coincide with the results of numerical simulation even disturbing parameter is of arbitrary magnitude. global bifurcation (dpeaa)DE-He213 strongly nonlinear (dpeaa)DE-He213 chaos (dpeaa)DE-He213 Melnikov method (dpeaa)DE-He213 Zhang, QiChang verfasserin aut Feng, JingJing verfasserin aut Enthalten in Science in China Heidelberg : Springer, 1997 54(2011), 8 vom: 24. Juni, Seite 1986-1991 (DE-627)385614756 (DE-600)2142897-9 1862-281X nnns volume:54 year:2011 number:8 day:24 month:06 pages:1986-1991 https://dx.doi.org/10.1007/s11431-011-4471-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 50.00 ASE AR 54 2011 8 24 06 1986-1991
language	English
source	Enthalten in Science in China 54(2011), 8 vom: 24. Juni, Seite 1986-1991 volume:54 year:2011 number:8 day:24 month:06 pages:1986-1991
sourceStr	Enthalten in Science in China 54(2011), 8 vom: 24. Juni, Seite 1986-1991 volume:54 year:2011 number:8 day:24 month:06 pages:1986-1991
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	global bifurcation strongly nonlinear chaos Melnikov method
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container_title	Science in China
authorswithroles_txt_mv	Wang, Wei @@aut@@ Zhang, QiChang @@aut@@ Feng, JingJing @@aut@@
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author	Wang, Wei
spellingShingle	Wang, Wei ddc 600 bkl 50.00 misc global bifurcation misc strongly nonlinear misc chaos misc Melnikov method Global bifurcations of strongly nonlinear oscillator induced by parametric and external excitation
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topic_title	600 ASE 50.00 bkl Global bifurcations of strongly nonlinear oscillator induced by parametric and external excitation global bifurcation (dpeaa)DE-He213 strongly nonlinear (dpeaa)DE-He213 chaos (dpeaa)DE-He213 Melnikov method (dpeaa)DE-He213
topic	ddc 600 bkl 50.00 misc global bifurcation misc strongly nonlinear misc chaos misc Melnikov method
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title	Global bifurcations of strongly nonlinear oscillator induced by parametric and external excitation
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title_full	Global bifurcations of strongly nonlinear oscillator induced by parametric and external excitation
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title_sort	global bifurcations of strongly nonlinear oscillator induced by parametric and external excitation
title_auth	Global bifurcations of strongly nonlinear oscillator induced by parametric and external excitation
abstract	Abstract The global bifurcation of strongly nonlinear oscillator induced by parametric and external excitation is researched. It is known that the parametric and external excitation may induce additional saddle states, and result in chaos in the phase space, which cannot be detected by applying the Melnikov method directly. A feasible solution for this problem is the combination of the averaged equations and Melnikov method. Therefore, we consider the averaged equations of the system subject to Duffing-Van der Pol strong nonlinearity by introducing the undetermined fundamental frequency. Then the bifurcation values of homoclinic structure formation are detected through the combined application of the new averaged equations with Melnikov integration. Finally, the explicit application shows the analytical conditions coincide with the results of numerical simulation even disturbing parameter is of arbitrary magnitude.
abstractGer	Abstract The global bifurcation of strongly nonlinear oscillator induced by parametric and external excitation is researched. It is known that the parametric and external excitation may induce additional saddle states, and result in chaos in the phase space, which cannot be detected by applying the Melnikov method directly. A feasible solution for this problem is the combination of the averaged equations and Melnikov method. Therefore, we consider the averaged equations of the system subject to Duffing-Van der Pol strong nonlinearity by introducing the undetermined fundamental frequency. Then the bifurcation values of homoclinic structure formation are detected through the combined application of the new averaged equations with Melnikov integration. Finally, the explicit application shows the analytical conditions coincide with the results of numerical simulation even disturbing parameter is of arbitrary magnitude.
abstract_unstemmed	Abstract The global bifurcation of strongly nonlinear oscillator induced by parametric and external excitation is researched. It is known that the parametric and external excitation may induce additional saddle states, and result in chaos in the phase space, which cannot be detected by applying the Melnikov method directly. A feasible solution for this problem is the combination of the averaged equations and Melnikov method. Therefore, we consider the averaged equations of the system subject to Duffing-Van der Pol strong nonlinearity by introducing the undetermined fundamental frequency. Then the bifurcation values of homoclinic structure formation are detected through the combined application of the new averaged equations with Melnikov integration. Finally, the explicit application shows the analytical conditions coincide with the results of numerical simulation even disturbing parameter is of arbitrary magnitude.
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title_short	Global bifurcations of strongly nonlinear oscillator induced by parametric and external excitation
url	https://dx.doi.org/10.1007/s11431-011-4471-4
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up_date	2024-07-04T00:54:43.869Z
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