Phase-coupled nonlinear dynamical systems, stability, first integrals, and Liapunov exponents
Abstract The stability of a class of coupled identical autonomous systems of first-order nonlinear ordinary differential equations is investigated. These couplings play a central role in controlling chaotic systems and can be applied in electronic circuits and laser systems. As applications we consi...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Steeb, W. -H. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1997 |
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| Schlagwörter: |
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| Anmerkung: |
© Plenum Publishing Corporation 1997 |
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| Übergeordnetes Werk: |
Enthalten in: International journal of theoretical physics - Kluwer Academic Publishers-Plenum Publishers, 1968, 36(1997), 10 vom: Okt., Seite 2043-2049 |
|---|---|
| Übergeordnetes Werk: |
volume:36 ; year:1997 ; number:10 ; month:10 ; pages:2043-2049 |
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| DOI / URN: |
10.1007/BF02435942 |
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| 520 | |a Abstract The stability of a class of coupled identical autonomous systems of first-order nonlinear ordinary differential equations is investigated. These couplings play a central role in controlling chaotic systems and can be applied in electronic circuits and laser systems. As applications we consider a coupled van der Pol equation and a coupled logistic map. When the uncoupled system admits a first integral we study whether a first integral exists for the coupled system. Gradient systems and the Painlevé property are also discussed. Finally, the relation of the Liapunov exponents of the uncoupled and coupled systems are discussed. | ||
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10.1007/BF02435942 doi (DE-627)OLC2052344527 (DE-He213)BF02435942-p DE-627 ger DE-627 rakwb eng 530 VZ 33.00 bkl Steeb, W. -H. verfasserin aut Phase-coupled nonlinear dynamical systems, stability, first integrals, and Liapunov exponents 1997 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1997 Abstract The stability of a class of coupled identical autonomous systems of first-order nonlinear ordinary differential equations is investigated. These couplings play a central role in controlling chaotic systems and can be applied in electronic circuits and laser systems. As applications we consider a coupled van der Pol equation and a coupled logistic map. When the uncoupled system admits a first integral we study whether a first integral exists for the coupled system. Gradient systems and the Painlevé property are also discussed. Finally, the relation of the Liapunov exponents of the uncoupled and coupled systems are discussed. Chaotic System Jacobian Matrix Hopf Bifurcation Couple System Gradient System van Wyk, M. A. aut Enthalten in International journal of theoretical physics Kluwer Academic Publishers-Plenum Publishers, 1968 36(1997), 10 vom: Okt., Seite 2043-2049 (DE-627)129546097 (DE-600)218277-4 (DE-576)014996413 0020-7748 nnns volume:36 year:1997 number:10 month:10 pages:2043-2049 https://doi.org/10.1007/BF02435942 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_11 GBV_ILN_20 GBV_ILN_32 GBV_ILN_40 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2021 GBV_ILN_2279 GBV_ILN_4012 GBV_ILN_4306 GBV_ILN_4310 GBV_ILN_4700 33.00 VZ AR 36 1997 10 10 2043-2049 |
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10.1007/BF02435942 doi (DE-627)OLC2052344527 (DE-He213)BF02435942-p DE-627 ger DE-627 rakwb eng 530 VZ 33.00 bkl Steeb, W. -H. verfasserin aut Phase-coupled nonlinear dynamical systems, stability, first integrals, and Liapunov exponents 1997 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1997 Abstract The stability of a class of coupled identical autonomous systems of first-order nonlinear ordinary differential equations is investigated. These couplings play a central role in controlling chaotic systems and can be applied in electronic circuits and laser systems. As applications we consider a coupled van der Pol equation and a coupled logistic map. When the uncoupled system admits a first integral we study whether a first integral exists for the coupled system. Gradient systems and the Painlevé property are also discussed. Finally, the relation of the Liapunov exponents of the uncoupled and coupled systems are discussed. Chaotic System Jacobian Matrix Hopf Bifurcation Couple System Gradient System van Wyk, M. A. aut Enthalten in International journal of theoretical physics Kluwer Academic Publishers-Plenum Publishers, 1968 36(1997), 10 vom: Okt., Seite 2043-2049 (DE-627)129546097 (DE-600)218277-4 (DE-576)014996413 0020-7748 nnns volume:36 year:1997 number:10 month:10 pages:2043-2049 https://doi.org/10.1007/BF02435942 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_11 GBV_ILN_20 GBV_ILN_32 GBV_ILN_40 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2021 GBV_ILN_2279 GBV_ILN_4012 GBV_ILN_4306 GBV_ILN_4310 GBV_ILN_4700 33.00 VZ AR 36 1997 10 10 2043-2049 |
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10.1007/BF02435942 doi (DE-627)OLC2052344527 (DE-He213)BF02435942-p DE-627 ger DE-627 rakwb eng 530 VZ 33.00 bkl Steeb, W. -H. verfasserin aut Phase-coupled nonlinear dynamical systems, stability, first integrals, and Liapunov exponents 1997 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1997 Abstract The stability of a class of coupled identical autonomous systems of first-order nonlinear ordinary differential equations is investigated. These couplings play a central role in controlling chaotic systems and can be applied in electronic circuits and laser systems. As applications we consider a coupled van der Pol equation and a coupled logistic map. When the uncoupled system admits a first integral we study whether a first integral exists for the coupled system. Gradient systems and the Painlevé property are also discussed. Finally, the relation of the Liapunov exponents of the uncoupled and coupled systems are discussed. Chaotic System Jacobian Matrix Hopf Bifurcation Couple System Gradient System van Wyk, M. A. aut Enthalten in International journal of theoretical physics Kluwer Academic Publishers-Plenum Publishers, 1968 36(1997), 10 vom: Okt., Seite 2043-2049 (DE-627)129546097 (DE-600)218277-4 (DE-576)014996413 0020-7748 nnns volume:36 year:1997 number:10 month:10 pages:2043-2049 https://doi.org/10.1007/BF02435942 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_11 GBV_ILN_20 GBV_ILN_32 GBV_ILN_40 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2021 GBV_ILN_2279 GBV_ILN_4012 GBV_ILN_4306 GBV_ILN_4310 GBV_ILN_4700 33.00 VZ AR 36 1997 10 10 2043-2049 |
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10.1007/BF02435942 doi (DE-627)OLC2052344527 (DE-He213)BF02435942-p DE-627 ger DE-627 rakwb eng 530 VZ 33.00 bkl Steeb, W. -H. verfasserin aut Phase-coupled nonlinear dynamical systems, stability, first integrals, and Liapunov exponents 1997 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1997 Abstract The stability of a class of coupled identical autonomous systems of first-order nonlinear ordinary differential equations is investigated. These couplings play a central role in controlling chaotic systems and can be applied in electronic circuits and laser systems. As applications we consider a coupled van der Pol equation and a coupled logistic map. When the uncoupled system admits a first integral we study whether a first integral exists for the coupled system. Gradient systems and the Painlevé property are also discussed. Finally, the relation of the Liapunov exponents of the uncoupled and coupled systems are discussed. Chaotic System Jacobian Matrix Hopf Bifurcation Couple System Gradient System van Wyk, M. A. aut Enthalten in International journal of theoretical physics Kluwer Academic Publishers-Plenum Publishers, 1968 36(1997), 10 vom: Okt., Seite 2043-2049 (DE-627)129546097 (DE-600)218277-4 (DE-576)014996413 0020-7748 nnns volume:36 year:1997 number:10 month:10 pages:2043-2049 https://doi.org/10.1007/BF02435942 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_11 GBV_ILN_20 GBV_ILN_32 GBV_ILN_40 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2021 GBV_ILN_2279 GBV_ILN_4012 GBV_ILN_4306 GBV_ILN_4310 GBV_ILN_4700 33.00 VZ AR 36 1997 10 10 2043-2049 |
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10.1007/BF02435942 doi (DE-627)OLC2052344527 (DE-He213)BF02435942-p DE-627 ger DE-627 rakwb eng 530 VZ 33.00 bkl Steeb, W. -H. verfasserin aut Phase-coupled nonlinear dynamical systems, stability, first integrals, and Liapunov exponents 1997 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Plenum Publishing Corporation 1997 Abstract The stability of a class of coupled identical autonomous systems of first-order nonlinear ordinary differential equations is investigated. These couplings play a central role in controlling chaotic systems and can be applied in electronic circuits and laser systems. As applications we consider a coupled van der Pol equation and a coupled logistic map. When the uncoupled system admits a first integral we study whether a first integral exists for the coupled system. Gradient systems and the Painlevé property are also discussed. Finally, the relation of the Liapunov exponents of the uncoupled and coupled systems are discussed. Chaotic System Jacobian Matrix Hopf Bifurcation Couple System Gradient System van Wyk, M. A. aut Enthalten in International journal of theoretical physics Kluwer Academic Publishers-Plenum Publishers, 1968 36(1997), 10 vom: Okt., Seite 2043-2049 (DE-627)129546097 (DE-600)218277-4 (DE-576)014996413 0020-7748 nnns volume:36 year:1997 number:10 month:10 pages:2043-2049 https://doi.org/10.1007/BF02435942 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_11 GBV_ILN_20 GBV_ILN_32 GBV_ILN_40 GBV_ILN_70 GBV_ILN_130 GBV_ILN_2021 GBV_ILN_2279 GBV_ILN_4012 GBV_ILN_4306 GBV_ILN_4310 GBV_ILN_4700 33.00 VZ AR 36 1997 10 10 2043-2049 |
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Abstract The stability of a class of coupled identical autonomous systems of first-order nonlinear ordinary differential equations is investigated. These couplings play a central role in controlling chaotic systems and can be applied in electronic circuits and laser systems. As applications we consider a coupled van der Pol equation and a coupled logistic map. When the uncoupled system admits a first integral we study whether a first integral exists for the coupled system. Gradient systems and the Painlevé property are also discussed. Finally, the relation of the Liapunov exponents of the uncoupled and coupled systems are discussed. © Plenum Publishing Corporation 1997 |
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Abstract The stability of a class of coupled identical autonomous systems of first-order nonlinear ordinary differential equations is investigated. These couplings play a central role in controlling chaotic systems and can be applied in electronic circuits and laser systems. As applications we consider a coupled van der Pol equation and a coupled logistic map. When the uncoupled system admits a first integral we study whether a first integral exists for the coupled system. Gradient systems and the Painlevé property are also discussed. Finally, the relation of the Liapunov exponents of the uncoupled and coupled systems are discussed. © Plenum Publishing Corporation 1997 |
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Abstract The stability of a class of coupled identical autonomous systems of first-order nonlinear ordinary differential equations is investigated. These couplings play a central role in controlling chaotic systems and can be applied in electronic circuits and laser systems. As applications we consider a coupled van der Pol equation and a coupled logistic map. When the uncoupled system admits a first integral we study whether a first integral exists for the coupled system. Gradient systems and the Painlevé property are also discussed. Finally, the relation of the Liapunov exponents of the uncoupled and coupled systems are discussed. © Plenum Publishing Corporation 1997 |
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Phase-coupled nonlinear dynamical systems, stability, first integrals, and Liapunov exponents |
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https://doi.org/10.1007/BF02435942 |
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van Wyk, M. A. |
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van Wyk, M. A. |
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129546097 |
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| doi_str |
10.1007/BF02435942 |
| up_date |
2024-07-03T14:44:46.225Z |
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1803569475069411328 |
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