Bifurcations and chaos of a discrete-time model in genetic regulatory networks
Abstract In this paper, the dynamics of a discrete-time genetic model is investigated. The existence and stability conditions of the fixed points are obtained. It is shown that the discrete-time genetic network undergoes fold bifurcation, flip bifurcation and Neimark–Sacker bifurcation. The biologic...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Yue, Dandan [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, 87(2016), 1 vom: 15. Sept., Seite 567-586 |
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| Übergeordnetes Werk: |
volume:87 ; year:2016 ; number:1 ; day:15 ; month:09 ; pages:567-586 |
| Links: |
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| DOI / URN: |
10.1007/s11071-016-3061-1 |
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OLC2051120129 |
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| 520 | |a Abstract In this paper, the dynamics of a discrete-time genetic model is investigated. The existence and stability conditions of the fixed points are obtained. It is shown that the discrete-time genetic network undergoes fold bifurcation, flip bifurcation and Neimark–Sacker bifurcation. The biological parameter and discretization step size are taken as bifurcation parameters, respectively, and the explicit bifurcation criteria are derived based on the center manifold theorem and bifurcation theory. Numerical simulations validate the theoretical analysis and also show that the system can exhibit diverse dynamic behaviors such as period-7, -14, -5, -10 orbits and chaos. The overall results reveal much richer dynamics of the discrete-time genetic model than that of the original continuous-time model. | ||
| 650 | 4 | |a Discrete-time genetic regulatory network | |
| 650 | 4 | |a Fold bifurcation | |
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| 700 | 1 | |a Ling, Guang |4 aut | |
| 700 | 1 | |a Wu, Yonghong |4 aut | |
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10.1007/s11071-016-3061-1 doi (DE-627)OLC2051120129 (DE-He213)s11071-016-3061-1-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Yue, Dandan verfasserin aut Bifurcations and chaos of a discrete-time model in genetic regulatory networks 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2016 Abstract In this paper, the dynamics of a discrete-time genetic model is investigated. The existence and stability conditions of the fixed points are obtained. It is shown that the discrete-time genetic network undergoes fold bifurcation, flip bifurcation and Neimark–Sacker bifurcation. The biological parameter and discretization step size are taken as bifurcation parameters, respectively, and the explicit bifurcation criteria are derived based on the center manifold theorem and bifurcation theory. Numerical simulations validate the theoretical analysis and also show that the system can exhibit diverse dynamic behaviors such as period-7, -14, -5, -10 orbits and chaos. The overall results reveal much richer dynamics of the discrete-time genetic model than that of the original continuous-time model. Discrete-time genetic regulatory network Fold bifurcation Flip bifurcation Neimark–Sacker bifurcation Chaos Guan, Zhi-Hong aut Chen, Jie aut Ling, Guang aut Wu, Yonghong aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 87(2016), 1 vom: 15. Sept., Seite 567-586 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:87 year:2016 number:1 day:15 month:09 pages:567-586 https://doi.org/10.1007/s11071-016-3061-1 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 87 2016 1 15 09 567-586 |
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10.1007/s11071-016-3061-1 doi (DE-627)OLC2051120129 (DE-He213)s11071-016-3061-1-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Yue, Dandan verfasserin aut Bifurcations and chaos of a discrete-time model in genetic regulatory networks 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2016 Abstract In this paper, the dynamics of a discrete-time genetic model is investigated. The existence and stability conditions of the fixed points are obtained. It is shown that the discrete-time genetic network undergoes fold bifurcation, flip bifurcation and Neimark–Sacker bifurcation. The biological parameter and discretization step size are taken as bifurcation parameters, respectively, and the explicit bifurcation criteria are derived based on the center manifold theorem and bifurcation theory. Numerical simulations validate the theoretical analysis and also show that the system can exhibit diverse dynamic behaviors such as period-7, -14, -5, -10 orbits and chaos. The overall results reveal much richer dynamics of the discrete-time genetic model than that of the original continuous-time model. Discrete-time genetic regulatory network Fold bifurcation Flip bifurcation Neimark–Sacker bifurcation Chaos Guan, Zhi-Hong aut Chen, Jie aut Ling, Guang aut Wu, Yonghong aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 87(2016), 1 vom: 15. Sept., Seite 567-586 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:87 year:2016 number:1 day:15 month:09 pages:567-586 https://doi.org/10.1007/s11071-016-3061-1 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 87 2016 1 15 09 567-586 |
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10.1007/s11071-016-3061-1 doi (DE-627)OLC2051120129 (DE-He213)s11071-016-3061-1-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Yue, Dandan verfasserin aut Bifurcations and chaos of a discrete-time model in genetic regulatory networks 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2016 Abstract In this paper, the dynamics of a discrete-time genetic model is investigated. The existence and stability conditions of the fixed points are obtained. It is shown that the discrete-time genetic network undergoes fold bifurcation, flip bifurcation and Neimark–Sacker bifurcation. The biological parameter and discretization step size are taken as bifurcation parameters, respectively, and the explicit bifurcation criteria are derived based on the center manifold theorem and bifurcation theory. Numerical simulations validate the theoretical analysis and also show that the system can exhibit diverse dynamic behaviors such as period-7, -14, -5, -10 orbits and chaos. The overall results reveal much richer dynamics of the discrete-time genetic model than that of the original continuous-time model. Discrete-time genetic regulatory network Fold bifurcation Flip bifurcation Neimark–Sacker bifurcation Chaos Guan, Zhi-Hong aut Chen, Jie aut Ling, Guang aut Wu, Yonghong aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 87(2016), 1 vom: 15. Sept., Seite 567-586 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:87 year:2016 number:1 day:15 month:09 pages:567-586 https://doi.org/10.1007/s11071-016-3061-1 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 87 2016 1 15 09 567-586 |
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10.1007/s11071-016-3061-1 doi (DE-627)OLC2051120129 (DE-He213)s11071-016-3061-1-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Yue, Dandan verfasserin aut Bifurcations and chaos of a discrete-time model in genetic regulatory networks 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2016 Abstract In this paper, the dynamics of a discrete-time genetic model is investigated. The existence and stability conditions of the fixed points are obtained. It is shown that the discrete-time genetic network undergoes fold bifurcation, flip bifurcation and Neimark–Sacker bifurcation. The biological parameter and discretization step size are taken as bifurcation parameters, respectively, and the explicit bifurcation criteria are derived based on the center manifold theorem and bifurcation theory. Numerical simulations validate the theoretical analysis and also show that the system can exhibit diverse dynamic behaviors such as period-7, -14, -5, -10 orbits and chaos. The overall results reveal much richer dynamics of the discrete-time genetic model than that of the original continuous-time model. Discrete-time genetic regulatory network Fold bifurcation Flip bifurcation Neimark–Sacker bifurcation Chaos Guan, Zhi-Hong aut Chen, Jie aut Ling, Guang aut Wu, Yonghong aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 87(2016), 1 vom: 15. Sept., Seite 567-586 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:87 year:2016 number:1 day:15 month:09 pages:567-586 https://doi.org/10.1007/s11071-016-3061-1 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 87 2016 1 15 09 567-586 |
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10.1007/s11071-016-3061-1 doi (DE-627)OLC2051120129 (DE-He213)s11071-016-3061-1-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Yue, Dandan verfasserin aut Bifurcations and chaos of a discrete-time model in genetic regulatory networks 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2016 Abstract In this paper, the dynamics of a discrete-time genetic model is investigated. The existence and stability conditions of the fixed points are obtained. It is shown that the discrete-time genetic network undergoes fold bifurcation, flip bifurcation and Neimark–Sacker bifurcation. The biological parameter and discretization step size are taken as bifurcation parameters, respectively, and the explicit bifurcation criteria are derived based on the center manifold theorem and bifurcation theory. Numerical simulations validate the theoretical analysis and also show that the system can exhibit diverse dynamic behaviors such as period-7, -14, -5, -10 orbits and chaos. The overall results reveal much richer dynamics of the discrete-time genetic model than that of the original continuous-time model. Discrete-time genetic regulatory network Fold bifurcation Flip bifurcation Neimark–Sacker bifurcation Chaos Guan, Zhi-Hong aut Chen, Jie aut Ling, Guang aut Wu, Yonghong aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 87(2016), 1 vom: 15. Sept., Seite 567-586 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:87 year:2016 number:1 day:15 month:09 pages:567-586 https://doi.org/10.1007/s11071-016-3061-1 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 87 2016 1 15 09 567-586 |
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Bifurcations and chaos of a discrete-time model in genetic regulatory networks |
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Abstract In this paper, the dynamics of a discrete-time genetic model is investigated. The existence and stability conditions of the fixed points are obtained. It is shown that the discrete-time genetic network undergoes fold bifurcation, flip bifurcation and Neimark–Sacker bifurcation. The biological parameter and discretization step size are taken as bifurcation parameters, respectively, and the explicit bifurcation criteria are derived based on the center manifold theorem and bifurcation theory. Numerical simulations validate the theoretical analysis and also show that the system can exhibit diverse dynamic behaviors such as period-7, -14, -5, -10 orbits and chaos. The overall results reveal much richer dynamics of the discrete-time genetic model than that of the original continuous-time model. © Springer Science+Business Media Dordrecht 2016 |
| abstractGer |
Abstract In this paper, the dynamics of a discrete-time genetic model is investigated. The existence and stability conditions of the fixed points are obtained. It is shown that the discrete-time genetic network undergoes fold bifurcation, flip bifurcation and Neimark–Sacker bifurcation. The biological parameter and discretization step size are taken as bifurcation parameters, respectively, and the explicit bifurcation criteria are derived based on the center manifold theorem and bifurcation theory. Numerical simulations validate the theoretical analysis and also show that the system can exhibit diverse dynamic behaviors such as period-7, -14, -5, -10 orbits and chaos. The overall results reveal much richer dynamics of the discrete-time genetic model than that of the original continuous-time model. © Springer Science+Business Media Dordrecht 2016 |
| abstract_unstemmed |
Abstract In this paper, the dynamics of a discrete-time genetic model is investigated. The existence and stability conditions of the fixed points are obtained. It is shown that the discrete-time genetic network undergoes fold bifurcation, flip bifurcation and Neimark–Sacker bifurcation. The biological parameter and discretization step size are taken as bifurcation parameters, respectively, and the explicit bifurcation criteria are derived based on the center manifold theorem and bifurcation theory. Numerical simulations validate the theoretical analysis and also show that the system can exhibit diverse dynamic behaviors such as period-7, -14, -5, -10 orbits and chaos. The overall results reveal much richer dynamics of the discrete-time genetic model than that of the original continuous-time model. © Springer Science+Business Media Dordrecht 2016 |
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Guan, Zhi-Hong Chen, Jie Ling, Guang Wu, Yonghong |
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Guan, Zhi-Hong Chen, Jie Ling, Guang Wu, Yonghong |
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130936782 |
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10.1007/s11071-016-3061-1 |
| up_date |
2024-07-04T03:37:40.593Z |
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