Symmetric periodic solutions of delay-coupled optoelectronic oscillators
Delay-coupled optoelectronic oscillators are considered. These structures are based on mutually coupled oscillators which oscillate at the same frequency. By taking the time delay as a bifurcation parameter, the stability of the zero equilibrium and the existence of Hopf bifurcations induced by dela...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Zhang, Chunrui [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016 |
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| Rechteinformationen: |
Nutzungsrecht: © The Author(s) 2016 |
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| Schlagwörter: |
Difference and Functional Equations Partial Differential Equations |
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| Übergeordnetes Werk: |
Enthalten in: Advances in difference equations - [Sylvania, Ohio] : Hindawi Publ. Corp., 2004, 2016(2016), 1, Seite 1-12 |
|---|---|
| Übergeordnetes Werk: |
volume:2016 ; year:2016 ; number:1 ; pages:1-12 |
| Links: |
|---|
| DOI / URN: |
10.1186/s13662-016-0755-0 |
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| Katalog-ID: |
OLC1974299139 |
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| 520 | |a Delay-coupled optoelectronic oscillators are considered. These structures are based on mutually coupled oscillators which oscillate at the same frequency. By taking the time delay as a bifurcation parameter, the stability of the zero equilibrium and the existence of Hopf bifurcations induced by delay are investigated, and then stability switches for the trivial solution are found. Conditions ensuring the stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Using the symmetric functional differential equation theories combined with the representation theory of Lie groups, the multiple Hopf bifurcations of the equilibrium are demonstrated. In particular, we find that the spatio-temporal patterns of bifurcating periodic oscillations will alternate according to the change of the propagation time delay in the coupling. The existence of multiple branches of bifurcating periodic solutions and their spatio-temporal patterns are obtained. Some numerical simulations are used to illustrate the effectiveness of the obtained results. | ||
| 540 | |a Nutzungsrecht: © The Author(s) 2016 | ||
| 650 | 4 | |a Difference and Functional Equations | |
| 650 | 4 | |a optoelectronic oscillators | |
| 650 | 4 | |a Partial Differential Equations | |
| 650 | 4 | |a Ordinary Differential Equations | |
| 650 | 4 | |a Analysis | |
| 650 | 4 | |a Functional Analysis | |
| 650 | 4 | |a spatio-temporal patterns | |
| 650 | 4 | |a stability | |
| 650 | 4 | |a symmetric bifurcation | |
| 650 | 4 | |a delay | |
| 650 | 4 | |a Mathematics, general | |
| 650 | 4 | |a Mathematics | |
| 700 | 1 | |a Li, Hongpeng |4 oth | |
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10.1186/s13662-016-0755-0 doi PQ20160430 (DE-627)OLC1974299139 (DE-599)GBVOLC1974299139 (PRQ)p1195-47616450288cd7b32b9cee2f92140479200e9d32148dccf011a41db8420917dd3 (KEY)0544041620160000016000100001symmetricperiodicsolutionsofdelaycoupledoptoelectr DE-627 ger DE-627 rakwb eng 510 ZDB 31.49 bkl Zhang, Chunrui verfasserin aut Symmetric periodic solutions of delay-coupled optoelectronic oscillators 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Delay-coupled optoelectronic oscillators are considered. These structures are based on mutually coupled oscillators which oscillate at the same frequency. By taking the time delay as a bifurcation parameter, the stability of the zero equilibrium and the existence of Hopf bifurcations induced by delay are investigated, and then stability switches for the trivial solution are found. Conditions ensuring the stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Using the symmetric functional differential equation theories combined with the representation theory of Lie groups, the multiple Hopf bifurcations of the equilibrium are demonstrated. In particular, we find that the spatio-temporal patterns of bifurcating periodic oscillations will alternate according to the change of the propagation time delay in the coupling. The existence of multiple branches of bifurcating periodic solutions and their spatio-temporal patterns are obtained. Some numerical simulations are used to illustrate the effectiveness of the obtained results. Nutzungsrecht: © The Author(s) 2016 Difference and Functional Equations optoelectronic oscillators Partial Differential Equations Ordinary Differential Equations Analysis Functional Analysis spatio-temporal patterns stability symmetric bifurcation delay Mathematics, general Mathematics Li, Hongpeng oth Enthalten in Advances in difference equations [Sylvania, Ohio] : Hindawi Publ. Corp., 2004 2016(2016), 1, Seite 1-12 (DE-627)394569423 (DE-600)2161260-2 (DE-576)9394569421 1687-1839 nnns volume:2016 year:2016 number:1 pages:1-12 http://dx.doi.org/10.1186/s13662-016-0755-0 Volltext http://search.proquest.com/docview/1771600603 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_4310 31.49 AVZ AR 2016 2016 1 1-12 |
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10.1186/s13662-016-0755-0 doi PQ20160430 (DE-627)OLC1974299139 (DE-599)GBVOLC1974299139 (PRQ)p1195-47616450288cd7b32b9cee2f92140479200e9d32148dccf011a41db8420917dd3 (KEY)0544041620160000016000100001symmetricperiodicsolutionsofdelaycoupledoptoelectr DE-627 ger DE-627 rakwb eng 510 ZDB 31.49 bkl Zhang, Chunrui verfasserin aut Symmetric periodic solutions of delay-coupled optoelectronic oscillators 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Delay-coupled optoelectronic oscillators are considered. These structures are based on mutually coupled oscillators which oscillate at the same frequency. By taking the time delay as a bifurcation parameter, the stability of the zero equilibrium and the existence of Hopf bifurcations induced by delay are investigated, and then stability switches for the trivial solution are found. Conditions ensuring the stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Using the symmetric functional differential equation theories combined with the representation theory of Lie groups, the multiple Hopf bifurcations of the equilibrium are demonstrated. In particular, we find that the spatio-temporal patterns of bifurcating periodic oscillations will alternate according to the change of the propagation time delay in the coupling. The existence of multiple branches of bifurcating periodic solutions and their spatio-temporal patterns are obtained. Some numerical simulations are used to illustrate the effectiveness of the obtained results. Nutzungsrecht: © The Author(s) 2016 Difference and Functional Equations optoelectronic oscillators Partial Differential Equations Ordinary Differential Equations Analysis Functional Analysis spatio-temporal patterns stability symmetric bifurcation delay Mathematics, general Mathematics Li, Hongpeng oth Enthalten in Advances in difference equations [Sylvania, Ohio] : Hindawi Publ. Corp., 2004 2016(2016), 1, Seite 1-12 (DE-627)394569423 (DE-600)2161260-2 (DE-576)9394569421 1687-1839 nnns volume:2016 year:2016 number:1 pages:1-12 http://dx.doi.org/10.1186/s13662-016-0755-0 Volltext http://search.proquest.com/docview/1771600603 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_4310 31.49 AVZ AR 2016 2016 1 1-12 |
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10.1186/s13662-016-0755-0 doi PQ20160430 (DE-627)OLC1974299139 (DE-599)GBVOLC1974299139 (PRQ)p1195-47616450288cd7b32b9cee2f92140479200e9d32148dccf011a41db8420917dd3 (KEY)0544041620160000016000100001symmetricperiodicsolutionsofdelaycoupledoptoelectr DE-627 ger DE-627 rakwb eng 510 ZDB 31.49 bkl Zhang, Chunrui verfasserin aut Symmetric periodic solutions of delay-coupled optoelectronic oscillators 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Delay-coupled optoelectronic oscillators are considered. These structures are based on mutually coupled oscillators which oscillate at the same frequency. By taking the time delay as a bifurcation parameter, the stability of the zero equilibrium and the existence of Hopf bifurcations induced by delay are investigated, and then stability switches for the trivial solution are found. Conditions ensuring the stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Using the symmetric functional differential equation theories combined with the representation theory of Lie groups, the multiple Hopf bifurcations of the equilibrium are demonstrated. In particular, we find that the spatio-temporal patterns of bifurcating periodic oscillations will alternate according to the change of the propagation time delay in the coupling. The existence of multiple branches of bifurcating periodic solutions and their spatio-temporal patterns are obtained. Some numerical simulations are used to illustrate the effectiveness of the obtained results. Nutzungsrecht: © The Author(s) 2016 Difference and Functional Equations optoelectronic oscillators Partial Differential Equations Ordinary Differential Equations Analysis Functional Analysis spatio-temporal patterns stability symmetric bifurcation delay Mathematics, general Mathematics Li, Hongpeng oth Enthalten in Advances in difference equations [Sylvania, Ohio] : Hindawi Publ. Corp., 2004 2016(2016), 1, Seite 1-12 (DE-627)394569423 (DE-600)2161260-2 (DE-576)9394569421 1687-1839 nnns volume:2016 year:2016 number:1 pages:1-12 http://dx.doi.org/10.1186/s13662-016-0755-0 Volltext http://search.proquest.com/docview/1771600603 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_4310 31.49 AVZ AR 2016 2016 1 1-12 |
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10.1186/s13662-016-0755-0 doi PQ20160430 (DE-627)OLC1974299139 (DE-599)GBVOLC1974299139 (PRQ)p1195-47616450288cd7b32b9cee2f92140479200e9d32148dccf011a41db8420917dd3 (KEY)0544041620160000016000100001symmetricperiodicsolutionsofdelaycoupledoptoelectr DE-627 ger DE-627 rakwb eng 510 ZDB 31.49 bkl Zhang, Chunrui verfasserin aut Symmetric periodic solutions of delay-coupled optoelectronic oscillators 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Delay-coupled optoelectronic oscillators are considered. These structures are based on mutually coupled oscillators which oscillate at the same frequency. By taking the time delay as a bifurcation parameter, the stability of the zero equilibrium and the existence of Hopf bifurcations induced by delay are investigated, and then stability switches for the trivial solution are found. Conditions ensuring the stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Using the symmetric functional differential equation theories combined with the representation theory of Lie groups, the multiple Hopf bifurcations of the equilibrium are demonstrated. In particular, we find that the spatio-temporal patterns of bifurcating periodic oscillations will alternate according to the change of the propagation time delay in the coupling. The existence of multiple branches of bifurcating periodic solutions and their spatio-temporal patterns are obtained. Some numerical simulations are used to illustrate the effectiveness of the obtained results. Nutzungsrecht: © The Author(s) 2016 Difference and Functional Equations optoelectronic oscillators Partial Differential Equations Ordinary Differential Equations Analysis Functional Analysis spatio-temporal patterns stability symmetric bifurcation delay Mathematics, general Mathematics Li, Hongpeng oth Enthalten in Advances in difference equations [Sylvania, Ohio] : Hindawi Publ. Corp., 2004 2016(2016), 1, Seite 1-12 (DE-627)394569423 (DE-600)2161260-2 (DE-576)9394569421 1687-1839 nnns volume:2016 year:2016 number:1 pages:1-12 http://dx.doi.org/10.1186/s13662-016-0755-0 Volltext http://search.proquest.com/docview/1771600603 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_4310 31.49 AVZ AR 2016 2016 1 1-12 |
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10.1186/s13662-016-0755-0 doi PQ20160430 (DE-627)OLC1974299139 (DE-599)GBVOLC1974299139 (PRQ)p1195-47616450288cd7b32b9cee2f92140479200e9d32148dccf011a41db8420917dd3 (KEY)0544041620160000016000100001symmetricperiodicsolutionsofdelaycoupledoptoelectr DE-627 ger DE-627 rakwb eng 510 ZDB 31.49 bkl Zhang, Chunrui verfasserin aut Symmetric periodic solutions of delay-coupled optoelectronic oscillators 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier Delay-coupled optoelectronic oscillators are considered. These structures are based on mutually coupled oscillators which oscillate at the same frequency. By taking the time delay as a bifurcation parameter, the stability of the zero equilibrium and the existence of Hopf bifurcations induced by delay are investigated, and then stability switches for the trivial solution are found. Conditions ensuring the stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Using the symmetric functional differential equation theories combined with the representation theory of Lie groups, the multiple Hopf bifurcations of the equilibrium are demonstrated. In particular, we find that the spatio-temporal patterns of bifurcating periodic oscillations will alternate according to the change of the propagation time delay in the coupling. The existence of multiple branches of bifurcating periodic solutions and their spatio-temporal patterns are obtained. Some numerical simulations are used to illustrate the effectiveness of the obtained results. Nutzungsrecht: © The Author(s) 2016 Difference and Functional Equations optoelectronic oscillators Partial Differential Equations Ordinary Differential Equations Analysis Functional Analysis spatio-temporal patterns stability symmetric bifurcation delay Mathematics, general Mathematics Li, Hongpeng oth Enthalten in Advances in difference equations [Sylvania, Ohio] : Hindawi Publ. Corp., 2004 2016(2016), 1, Seite 1-12 (DE-627)394569423 (DE-600)2161260-2 (DE-576)9394569421 1687-1839 nnns volume:2016 year:2016 number:1 pages:1-12 http://dx.doi.org/10.1186/s13662-016-0755-0 Volltext http://search.proquest.com/docview/1771600603 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_4310 31.49 AVZ AR 2016 2016 1 1-12 |
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Symmetric periodic solutions of delay-coupled optoelectronic oscillators |
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Zhang, Chunrui |
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Advances in difference equations |
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510 |
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symmetric periodic solutions of delay-coupled optoelectronic oscillators |
| title_auth |
Symmetric periodic solutions of delay-coupled optoelectronic oscillators |
| abstract |
Delay-coupled optoelectronic oscillators are considered. These structures are based on mutually coupled oscillators which oscillate at the same frequency. By taking the time delay as a bifurcation parameter, the stability of the zero equilibrium and the existence of Hopf bifurcations induced by delay are investigated, and then stability switches for the trivial solution are found. Conditions ensuring the stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Using the symmetric functional differential equation theories combined with the representation theory of Lie groups, the multiple Hopf bifurcations of the equilibrium are demonstrated. In particular, we find that the spatio-temporal patterns of bifurcating periodic oscillations will alternate according to the change of the propagation time delay in the coupling. The existence of multiple branches of bifurcating periodic solutions and their spatio-temporal patterns are obtained. Some numerical simulations are used to illustrate the effectiveness of the obtained results. |
| abstractGer |
Delay-coupled optoelectronic oscillators are considered. These structures are based on mutually coupled oscillators which oscillate at the same frequency. By taking the time delay as a bifurcation parameter, the stability of the zero equilibrium and the existence of Hopf bifurcations induced by delay are investigated, and then stability switches for the trivial solution are found. Conditions ensuring the stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Using the symmetric functional differential equation theories combined with the representation theory of Lie groups, the multiple Hopf bifurcations of the equilibrium are demonstrated. In particular, we find that the spatio-temporal patterns of bifurcating periodic oscillations will alternate according to the change of the propagation time delay in the coupling. The existence of multiple branches of bifurcating periodic solutions and their spatio-temporal patterns are obtained. Some numerical simulations are used to illustrate the effectiveness of the obtained results. |
| abstract_unstemmed |
Delay-coupled optoelectronic oscillators are considered. These structures are based on mutually coupled oscillators which oscillate at the same frequency. By taking the time delay as a bifurcation parameter, the stability of the zero equilibrium and the existence of Hopf bifurcations induced by delay are investigated, and then stability switches for the trivial solution are found. Conditions ensuring the stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Using the symmetric functional differential equation theories combined with the representation theory of Lie groups, the multiple Hopf bifurcations of the equilibrium are demonstrated. In particular, we find that the spatio-temporal patterns of bifurcating periodic oscillations will alternate according to the change of the propagation time delay in the coupling. The existence of multiple branches of bifurcating periodic solutions and their spatio-temporal patterns are obtained. Some numerical simulations are used to illustrate the effectiveness of the obtained results. |
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| title_short |
Symmetric periodic solutions of delay-coupled optoelectronic oscillators |
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http://dx.doi.org/10.1186/s13662-016-0755-0 http://search.proquest.com/docview/1771600603 |
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2024-07-04T04:11:42.353Z |
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