The mechanism of bursting oscillations with different codimensional bifurcations and nonlinear structures
Abstract The main purpose of this article is to demonstrate that bursting oscillations can be observed not only in the slow–fast autonomous dynamical systems with multiple scales associated with time domain, but also in the non-autonomous dynamical systems with periodic excitations when an order gap...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Bi, Qinsheng [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media Dordrecht 2016 |
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| Übergeordnetes Werk: |
Enthalten in: Nonlinear dynamics - Springer Netherlands, 1990, 85(2016), 2 vom: 06. Apr., Seite 993-1005 |
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| Übergeordnetes Werk: |
volume:85 ; year:2016 ; number:2 ; day:06 ; month:04 ; pages:993-1005 |
| Links: |
|---|
| DOI / URN: |
10.1007/s11071-016-2738-9 |
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| Katalog-ID: |
OLC2051116903 |
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| 520 | |a Abstract The main purpose of this article is to demonstrate that bursting oscillations can be observed not only in the slow–fast autonomous dynamical systems with multiple scales associated with time domain, but also in the non-autonomous dynamical systems with periodic excitations when an order gap exists between the exciting frequency and the natural frequency, implying multiple scales in frequency domain. Furthermore, we try to investigate the influence of different codimensional bifurcations between the quiescent states (QS) and repetitive spiking states (SP) and the nonlinear structures with different equilibrium branches on the bursting oscillations. By introducing an inductor as well as a periodically changed electrical current source in a traditional Chua’s circuit and taking suitable parameter values, a modified four-dimensional periodically excited oscillator with multiple scales in frequency domain is established. Bursting oscillations for two cases with nonlinear terms up to third and fifth order with codimension-1 and codimension-2 bifurcations have been explored, respectively. It is found that more equilibrium states may exist when higher order nonlinear terms are introduced in the vector field, which may cause multiple quiescent states, and accordingly, multiple forms of repetitive spiking oscillations in one bursting attractor, leading to more complicated bursting phenomena. Furthermore, instead of jumping from one stable equilibrium branch to settle down to another stable equilibrium branch when codimension-1 bifurcations (fold bifurcations) exist between QSs and SPs, codimension-2 bifurcation (fold-Hopf bifurcation) may cause QS approximately located on one stable equilibrium branch to jump to repetitive spiking oscillations surrounding another stable equilibrium branch of the generalized autonomous system. | ||
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10.1007/s11071-016-2738-9 doi (DE-627)OLC2051116903 (DE-He213)s11071-016-2738-9-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Bi, Qinsheng verfasserin aut The mechanism of bursting oscillations with different codimensional bifurcations and nonlinear structures 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2016 Abstract The main purpose of this article is to demonstrate that bursting oscillations can be observed not only in the slow–fast autonomous dynamical systems with multiple scales associated with time domain, but also in the non-autonomous dynamical systems with periodic excitations when an order gap exists between the exciting frequency and the natural frequency, implying multiple scales in frequency domain. Furthermore, we try to investigate the influence of different codimensional bifurcations between the quiescent states (QS) and repetitive spiking states (SP) and the nonlinear structures with different equilibrium branches on the bursting oscillations. By introducing an inductor as well as a periodically changed electrical current source in a traditional Chua’s circuit and taking suitable parameter values, a modified four-dimensional periodically excited oscillator with multiple scales in frequency domain is established. Bursting oscillations for two cases with nonlinear terms up to third and fifth order with codimension-1 and codimension-2 bifurcations have been explored, respectively. It is found that more equilibrium states may exist when higher order nonlinear terms are introduced in the vector field, which may cause multiple quiescent states, and accordingly, multiple forms of repetitive spiking oscillations in one bursting attractor, leading to more complicated bursting phenomena. Furthermore, instead of jumping from one stable equilibrium branch to settle down to another stable equilibrium branch when codimension-1 bifurcations (fold bifurcations) exist between QSs and SPs, codimension-2 bifurcation (fold-Hopf bifurcation) may cause QS approximately located on one stable equilibrium branch to jump to repetitive spiking oscillations surrounding another stable equilibrium branch of the generalized autonomous system. Periodic excitation Multiple time scales Bursting oscillation Bifurcation mechanism Li, Shaolong aut Kurths, Juergen aut Zhang, Zhengdi aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 85(2016), 2 vom: 06. Apr., Seite 993-1005 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:85 year:2016 number:2 day:06 month:04 pages:993-1005 https://doi.org/10.1007/s11071-016-2738-9 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 85 2016 2 06 04 993-1005 |
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10.1007/s11071-016-2738-9 doi (DE-627)OLC2051116903 (DE-He213)s11071-016-2738-9-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Bi, Qinsheng verfasserin aut The mechanism of bursting oscillations with different codimensional bifurcations and nonlinear structures 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2016 Abstract The main purpose of this article is to demonstrate that bursting oscillations can be observed not only in the slow–fast autonomous dynamical systems with multiple scales associated with time domain, but also in the non-autonomous dynamical systems with periodic excitations when an order gap exists between the exciting frequency and the natural frequency, implying multiple scales in frequency domain. Furthermore, we try to investigate the influence of different codimensional bifurcations between the quiescent states (QS) and repetitive spiking states (SP) and the nonlinear structures with different equilibrium branches on the bursting oscillations. By introducing an inductor as well as a periodically changed electrical current source in a traditional Chua’s circuit and taking suitable parameter values, a modified four-dimensional periodically excited oscillator with multiple scales in frequency domain is established. Bursting oscillations for two cases with nonlinear terms up to third and fifth order with codimension-1 and codimension-2 bifurcations have been explored, respectively. It is found that more equilibrium states may exist when higher order nonlinear terms are introduced in the vector field, which may cause multiple quiescent states, and accordingly, multiple forms of repetitive spiking oscillations in one bursting attractor, leading to more complicated bursting phenomena. Furthermore, instead of jumping from one stable equilibrium branch to settle down to another stable equilibrium branch when codimension-1 bifurcations (fold bifurcations) exist between QSs and SPs, codimension-2 bifurcation (fold-Hopf bifurcation) may cause QS approximately located on one stable equilibrium branch to jump to repetitive spiking oscillations surrounding another stable equilibrium branch of the generalized autonomous system. Periodic excitation Multiple time scales Bursting oscillation Bifurcation mechanism Li, Shaolong aut Kurths, Juergen aut Zhang, Zhengdi aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 85(2016), 2 vom: 06. Apr., Seite 993-1005 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:85 year:2016 number:2 day:06 month:04 pages:993-1005 https://doi.org/10.1007/s11071-016-2738-9 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 85 2016 2 06 04 993-1005 |
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10.1007/s11071-016-2738-9 doi (DE-627)OLC2051116903 (DE-He213)s11071-016-2738-9-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Bi, Qinsheng verfasserin aut The mechanism of bursting oscillations with different codimensional bifurcations and nonlinear structures 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2016 Abstract The main purpose of this article is to demonstrate that bursting oscillations can be observed not only in the slow–fast autonomous dynamical systems with multiple scales associated with time domain, but also in the non-autonomous dynamical systems with periodic excitations when an order gap exists between the exciting frequency and the natural frequency, implying multiple scales in frequency domain. Furthermore, we try to investigate the influence of different codimensional bifurcations between the quiescent states (QS) and repetitive spiking states (SP) and the nonlinear structures with different equilibrium branches on the bursting oscillations. By introducing an inductor as well as a periodically changed electrical current source in a traditional Chua’s circuit and taking suitable parameter values, a modified four-dimensional periodically excited oscillator with multiple scales in frequency domain is established. Bursting oscillations for two cases with nonlinear terms up to third and fifth order with codimension-1 and codimension-2 bifurcations have been explored, respectively. It is found that more equilibrium states may exist when higher order nonlinear terms are introduced in the vector field, which may cause multiple quiescent states, and accordingly, multiple forms of repetitive spiking oscillations in one bursting attractor, leading to more complicated bursting phenomena. Furthermore, instead of jumping from one stable equilibrium branch to settle down to another stable equilibrium branch when codimension-1 bifurcations (fold bifurcations) exist between QSs and SPs, codimension-2 bifurcation (fold-Hopf bifurcation) may cause QS approximately located on one stable equilibrium branch to jump to repetitive spiking oscillations surrounding another stable equilibrium branch of the generalized autonomous system. Periodic excitation Multiple time scales Bursting oscillation Bifurcation mechanism Li, Shaolong aut Kurths, Juergen aut Zhang, Zhengdi aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 85(2016), 2 vom: 06. Apr., Seite 993-1005 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:85 year:2016 number:2 day:06 month:04 pages:993-1005 https://doi.org/10.1007/s11071-016-2738-9 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 85 2016 2 06 04 993-1005 |
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10.1007/s11071-016-2738-9 doi (DE-627)OLC2051116903 (DE-He213)s11071-016-2738-9-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Bi, Qinsheng verfasserin aut The mechanism of bursting oscillations with different codimensional bifurcations and nonlinear structures 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2016 Abstract The main purpose of this article is to demonstrate that bursting oscillations can be observed not only in the slow–fast autonomous dynamical systems with multiple scales associated with time domain, but also in the non-autonomous dynamical systems with periodic excitations when an order gap exists between the exciting frequency and the natural frequency, implying multiple scales in frequency domain. Furthermore, we try to investigate the influence of different codimensional bifurcations between the quiescent states (QS) and repetitive spiking states (SP) and the nonlinear structures with different equilibrium branches on the bursting oscillations. By introducing an inductor as well as a periodically changed electrical current source in a traditional Chua’s circuit and taking suitable parameter values, a modified four-dimensional periodically excited oscillator with multiple scales in frequency domain is established. Bursting oscillations for two cases with nonlinear terms up to third and fifth order with codimension-1 and codimension-2 bifurcations have been explored, respectively. It is found that more equilibrium states may exist when higher order nonlinear terms are introduced in the vector field, which may cause multiple quiescent states, and accordingly, multiple forms of repetitive spiking oscillations in one bursting attractor, leading to more complicated bursting phenomena. Furthermore, instead of jumping from one stable equilibrium branch to settle down to another stable equilibrium branch when codimension-1 bifurcations (fold bifurcations) exist between QSs and SPs, codimension-2 bifurcation (fold-Hopf bifurcation) may cause QS approximately located on one stable equilibrium branch to jump to repetitive spiking oscillations surrounding another stable equilibrium branch of the generalized autonomous system. Periodic excitation Multiple time scales Bursting oscillation Bifurcation mechanism Li, Shaolong aut Kurths, Juergen aut Zhang, Zhengdi aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 85(2016), 2 vom: 06. Apr., Seite 993-1005 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:85 year:2016 number:2 day:06 month:04 pages:993-1005 https://doi.org/10.1007/s11071-016-2738-9 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 85 2016 2 06 04 993-1005 |
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The mechanism of bursting oscillations with different codimensional bifurcations and nonlinear structures |
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| title_full |
The mechanism of bursting oscillations with different codimensional bifurcations and nonlinear structures |
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Bi, Qinsheng |
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Nonlinear dynamics |
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Nonlinear dynamics |
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eng |
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500 - Science |
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marc |
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2016 |
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993 |
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Bi, Qinsheng Li, Shaolong Kurths, Juergen Zhang, Zhengdi |
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85 |
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Aufsätze |
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Bi, Qinsheng |
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10.1007/s11071-016-2738-9 |
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510 |
| title_sort |
the mechanism of bursting oscillations with different codimensional bifurcations and nonlinear structures |
| title_auth |
The mechanism of bursting oscillations with different codimensional bifurcations and nonlinear structures |
| abstract |
Abstract The main purpose of this article is to demonstrate that bursting oscillations can be observed not only in the slow–fast autonomous dynamical systems with multiple scales associated with time domain, but also in the non-autonomous dynamical systems with periodic excitations when an order gap exists between the exciting frequency and the natural frequency, implying multiple scales in frequency domain. Furthermore, we try to investigate the influence of different codimensional bifurcations between the quiescent states (QS) and repetitive spiking states (SP) and the nonlinear structures with different equilibrium branches on the bursting oscillations. By introducing an inductor as well as a periodically changed electrical current source in a traditional Chua’s circuit and taking suitable parameter values, a modified four-dimensional periodically excited oscillator with multiple scales in frequency domain is established. Bursting oscillations for two cases with nonlinear terms up to third and fifth order with codimension-1 and codimension-2 bifurcations have been explored, respectively. It is found that more equilibrium states may exist when higher order nonlinear terms are introduced in the vector field, which may cause multiple quiescent states, and accordingly, multiple forms of repetitive spiking oscillations in one bursting attractor, leading to more complicated bursting phenomena. Furthermore, instead of jumping from one stable equilibrium branch to settle down to another stable equilibrium branch when codimension-1 bifurcations (fold bifurcations) exist between QSs and SPs, codimension-2 bifurcation (fold-Hopf bifurcation) may cause QS approximately located on one stable equilibrium branch to jump to repetitive spiking oscillations surrounding another stable equilibrium branch of the generalized autonomous system. © Springer Science+Business Media Dordrecht 2016 |
| abstractGer |
Abstract The main purpose of this article is to demonstrate that bursting oscillations can be observed not only in the slow–fast autonomous dynamical systems with multiple scales associated with time domain, but also in the non-autonomous dynamical systems with periodic excitations when an order gap exists between the exciting frequency and the natural frequency, implying multiple scales in frequency domain. Furthermore, we try to investigate the influence of different codimensional bifurcations between the quiescent states (QS) and repetitive spiking states (SP) and the nonlinear structures with different equilibrium branches on the bursting oscillations. By introducing an inductor as well as a periodically changed electrical current source in a traditional Chua’s circuit and taking suitable parameter values, a modified four-dimensional periodically excited oscillator with multiple scales in frequency domain is established. Bursting oscillations for two cases with nonlinear terms up to third and fifth order with codimension-1 and codimension-2 bifurcations have been explored, respectively. It is found that more equilibrium states may exist when higher order nonlinear terms are introduced in the vector field, which may cause multiple quiescent states, and accordingly, multiple forms of repetitive spiking oscillations in one bursting attractor, leading to more complicated bursting phenomena. Furthermore, instead of jumping from one stable equilibrium branch to settle down to another stable equilibrium branch when codimension-1 bifurcations (fold bifurcations) exist between QSs and SPs, codimension-2 bifurcation (fold-Hopf bifurcation) may cause QS approximately located on one stable equilibrium branch to jump to repetitive spiking oscillations surrounding another stable equilibrium branch of the generalized autonomous system. © Springer Science+Business Media Dordrecht 2016 |
| abstract_unstemmed |
Abstract The main purpose of this article is to demonstrate that bursting oscillations can be observed not only in the slow–fast autonomous dynamical systems with multiple scales associated with time domain, but also in the non-autonomous dynamical systems with periodic excitations when an order gap exists between the exciting frequency and the natural frequency, implying multiple scales in frequency domain. Furthermore, we try to investigate the influence of different codimensional bifurcations between the quiescent states (QS) and repetitive spiking states (SP) and the nonlinear structures with different equilibrium branches on the bursting oscillations. By introducing an inductor as well as a periodically changed electrical current source in a traditional Chua’s circuit and taking suitable parameter values, a modified four-dimensional periodically excited oscillator with multiple scales in frequency domain is established. Bursting oscillations for two cases with nonlinear terms up to third and fifth order with codimension-1 and codimension-2 bifurcations have been explored, respectively. It is found that more equilibrium states may exist when higher order nonlinear terms are introduced in the vector field, which may cause multiple quiescent states, and accordingly, multiple forms of repetitive spiking oscillations in one bursting attractor, leading to more complicated bursting phenomena. Furthermore, instead of jumping from one stable equilibrium branch to settle down to another stable equilibrium branch when codimension-1 bifurcations (fold bifurcations) exist between QSs and SPs, codimension-2 bifurcation (fold-Hopf bifurcation) may cause QS approximately located on one stable equilibrium branch to jump to repetitive spiking oscillations surrounding another stable equilibrium branch of the generalized autonomous system. © Springer Science+Business Media Dordrecht 2016 |
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| title_short |
The mechanism of bursting oscillations with different codimensional bifurcations and nonlinear structures |
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https://doi.org/10.1007/s11071-016-2738-9 |
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Li, Shaolong Kurths, Juergen Zhang, Zhengdi |
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2024-07-04T03:37:14.797Z |
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