Patterns of interaction of coupled reaction–diffusion systems of the FitzHugh–Nagumo type
Abstract Motivated by the dynamics of neuronal responses, we analyze the dynamics of the FitzHugh–Nagumo slow–fast system with diffusion and coupling. In the case of diffusion, the system provides a canonical example of Turing–Hopf bifurcation. By analyzing the linear stability of the local equilibr...
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Gespeichert in:
| Autor*in: |
Zhang, Chunrui [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2019 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Nature B.V. 2019 |
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| Übergeordnetes Werk: |
Enthalten in: Nonlinear dynamics - Springer Netherlands, 1990, 97(2019), 2 vom: 21. Juni, Seite 1451-1476 |
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| Übergeordnetes Werk: |
volume:97 ; year:2019 ; number:2 ; day:21 ; month:06 ; pages:1451-1476 |
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| DOI / URN: |
10.1007/s11071-019-05065-8 |
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| 520 | |a Abstract Motivated by the dynamics of neuronal responses, we analyze the dynamics of the FitzHugh–Nagumo slow–fast system with diffusion and coupling. In the case of diffusion, the system provides a canonical example of Turing–Hopf bifurcation. By analyzing the linear stability of the local equilibrium, the occurrence of Turing–Hopf bifurcation, Turing–Turing bifurcation and coupled Turing–Hopf bifurcation are obtained. The normal form associated with the Turing–Hopf bifurcation is obtained by using the procedure of Song for calculating the normal form of PDEs. Further, in the case of two coupled FitzHugh–Nagumo reaction–diffusion, the Turing–Hopf–Turing bifurcation occurs, and we also find the case about the spatial resonance of Turing–Turing bifurcation arising, and two kinds spatially steady-state solutions are found which are synchronous or anti-phased. Finally, sample numerical results are reported. | ||
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10.1007/s11071-019-05065-8 doi (DE-627)OLC2051139717 (DE-He213)s11071-019-05065-8-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Zhang, Chunrui verfasserin aut Patterns of interaction of coupled reaction–diffusion systems of the FitzHugh–Nagumo type 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Nature B.V. 2019 Abstract Motivated by the dynamics of neuronal responses, we analyze the dynamics of the FitzHugh–Nagumo slow–fast system with diffusion and coupling. In the case of diffusion, the system provides a canonical example of Turing–Hopf bifurcation. By analyzing the linear stability of the local equilibrium, the occurrence of Turing–Hopf bifurcation, Turing–Turing bifurcation and coupled Turing–Hopf bifurcation are obtained. The normal form associated with the Turing–Hopf bifurcation is obtained by using the procedure of Song for calculating the normal form of PDEs. Further, in the case of two coupled FitzHugh–Nagumo reaction–diffusion, the Turing–Hopf–Turing bifurcation occurs, and we also find the case about the spatial resonance of Turing–Turing bifurcation arising, and two kinds spatially steady-state solutions are found which are synchronous or anti-phased. Finally, sample numerical results are reported. FitzHugh–Nagumo Diffusion Coupling Turing–Hopf bifurcation Turing–Hopf–Turing bifurcation Spatial resonance Normal forms Ke, Ai aut Zheng, Baodong aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 97(2019), 2 vom: 21. Juni, Seite 1451-1476 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:97 year:2019 number:2 day:21 month:06 pages:1451-1476 https://doi.org/10.1007/s11071-019-05065-8 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 97 2019 2 21 06 1451-1476 |
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10.1007/s11071-019-05065-8 doi (DE-627)OLC2051139717 (DE-He213)s11071-019-05065-8-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Zhang, Chunrui verfasserin aut Patterns of interaction of coupled reaction–diffusion systems of the FitzHugh–Nagumo type 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Nature B.V. 2019 Abstract Motivated by the dynamics of neuronal responses, we analyze the dynamics of the FitzHugh–Nagumo slow–fast system with diffusion and coupling. In the case of diffusion, the system provides a canonical example of Turing–Hopf bifurcation. By analyzing the linear stability of the local equilibrium, the occurrence of Turing–Hopf bifurcation, Turing–Turing bifurcation and coupled Turing–Hopf bifurcation are obtained. The normal form associated with the Turing–Hopf bifurcation is obtained by using the procedure of Song for calculating the normal form of PDEs. Further, in the case of two coupled FitzHugh–Nagumo reaction–diffusion, the Turing–Hopf–Turing bifurcation occurs, and we also find the case about the spatial resonance of Turing–Turing bifurcation arising, and two kinds spatially steady-state solutions are found which are synchronous or anti-phased. Finally, sample numerical results are reported. FitzHugh–Nagumo Diffusion Coupling Turing–Hopf bifurcation Turing–Hopf–Turing bifurcation Spatial resonance Normal forms Ke, Ai aut Zheng, Baodong aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 97(2019), 2 vom: 21. Juni, Seite 1451-1476 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:97 year:2019 number:2 day:21 month:06 pages:1451-1476 https://doi.org/10.1007/s11071-019-05065-8 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 97 2019 2 21 06 1451-1476 |
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10.1007/s11071-019-05065-8 doi (DE-627)OLC2051139717 (DE-He213)s11071-019-05065-8-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Zhang, Chunrui verfasserin aut Patterns of interaction of coupled reaction–diffusion systems of the FitzHugh–Nagumo type 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Nature B.V. 2019 Abstract Motivated by the dynamics of neuronal responses, we analyze the dynamics of the FitzHugh–Nagumo slow–fast system with diffusion and coupling. In the case of diffusion, the system provides a canonical example of Turing–Hopf bifurcation. By analyzing the linear stability of the local equilibrium, the occurrence of Turing–Hopf bifurcation, Turing–Turing bifurcation and coupled Turing–Hopf bifurcation are obtained. The normal form associated with the Turing–Hopf bifurcation is obtained by using the procedure of Song for calculating the normal form of PDEs. Further, in the case of two coupled FitzHugh–Nagumo reaction–diffusion, the Turing–Hopf–Turing bifurcation occurs, and we also find the case about the spatial resonance of Turing–Turing bifurcation arising, and two kinds spatially steady-state solutions are found which are synchronous or anti-phased. Finally, sample numerical results are reported. FitzHugh–Nagumo Diffusion Coupling Turing–Hopf bifurcation Turing–Hopf–Turing bifurcation Spatial resonance Normal forms Ke, Ai aut Zheng, Baodong aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 97(2019), 2 vom: 21. Juni, Seite 1451-1476 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:97 year:2019 number:2 day:21 month:06 pages:1451-1476 https://doi.org/10.1007/s11071-019-05065-8 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 97 2019 2 21 06 1451-1476 |
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10.1007/s11071-019-05065-8 doi (DE-627)OLC2051139717 (DE-He213)s11071-019-05065-8-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Zhang, Chunrui verfasserin aut Patterns of interaction of coupled reaction–diffusion systems of the FitzHugh–Nagumo type 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Nature B.V. 2019 Abstract Motivated by the dynamics of neuronal responses, we analyze the dynamics of the FitzHugh–Nagumo slow–fast system with diffusion and coupling. In the case of diffusion, the system provides a canonical example of Turing–Hopf bifurcation. By analyzing the linear stability of the local equilibrium, the occurrence of Turing–Hopf bifurcation, Turing–Turing bifurcation and coupled Turing–Hopf bifurcation are obtained. The normal form associated with the Turing–Hopf bifurcation is obtained by using the procedure of Song for calculating the normal form of PDEs. Further, in the case of two coupled FitzHugh–Nagumo reaction–diffusion, the Turing–Hopf–Turing bifurcation occurs, and we also find the case about the spatial resonance of Turing–Turing bifurcation arising, and two kinds spatially steady-state solutions are found which are synchronous or anti-phased. Finally, sample numerical results are reported. FitzHugh–Nagumo Diffusion Coupling Turing–Hopf bifurcation Turing–Hopf–Turing bifurcation Spatial resonance Normal forms Ke, Ai aut Zheng, Baodong aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 97(2019), 2 vom: 21. Juni, Seite 1451-1476 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:97 year:2019 number:2 day:21 month:06 pages:1451-1476 https://doi.org/10.1007/s11071-019-05065-8 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 97 2019 2 21 06 1451-1476 |
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10.1007/s11071-019-05065-8 doi (DE-627)OLC2051139717 (DE-He213)s11071-019-05065-8-p DE-627 ger DE-627 rakwb eng 510 VZ 11 ssgn Zhang, Chunrui verfasserin aut Patterns of interaction of coupled reaction–diffusion systems of the FitzHugh–Nagumo type 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Nature B.V. 2019 Abstract Motivated by the dynamics of neuronal responses, we analyze the dynamics of the FitzHugh–Nagumo slow–fast system with diffusion and coupling. In the case of diffusion, the system provides a canonical example of Turing–Hopf bifurcation. By analyzing the linear stability of the local equilibrium, the occurrence of Turing–Hopf bifurcation, Turing–Turing bifurcation and coupled Turing–Hopf bifurcation are obtained. The normal form associated with the Turing–Hopf bifurcation is obtained by using the procedure of Song for calculating the normal form of PDEs. Further, in the case of two coupled FitzHugh–Nagumo reaction–diffusion, the Turing–Hopf–Turing bifurcation occurs, and we also find the case about the spatial resonance of Turing–Turing bifurcation arising, and two kinds spatially steady-state solutions are found which are synchronous or anti-phased. Finally, sample numerical results are reported. FitzHugh–Nagumo Diffusion Coupling Turing–Hopf bifurcation Turing–Hopf–Turing bifurcation Spatial resonance Normal forms Ke, Ai aut Zheng, Baodong aut Enthalten in Nonlinear dynamics Springer Netherlands, 1990 97(2019), 2 vom: 21. Juni, Seite 1451-1476 (DE-627)130936782 (DE-600)1058624-6 (DE-576)034188126 0924-090X nnns volume:97 year:2019 number:2 day:21 month:06 pages:1451-1476 https://doi.org/10.1007/s11071-019-05065-8 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 97 2019 2 21 06 1451-1476 |
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Patterns of interaction of coupled reaction–diffusion systems of the FitzHugh–Nagumo type |
| abstract |
Abstract Motivated by the dynamics of neuronal responses, we analyze the dynamics of the FitzHugh–Nagumo slow–fast system with diffusion and coupling. In the case of diffusion, the system provides a canonical example of Turing–Hopf bifurcation. By analyzing the linear stability of the local equilibrium, the occurrence of Turing–Hopf bifurcation, Turing–Turing bifurcation and coupled Turing–Hopf bifurcation are obtained. The normal form associated with the Turing–Hopf bifurcation is obtained by using the procedure of Song for calculating the normal form of PDEs. Further, in the case of two coupled FitzHugh–Nagumo reaction–diffusion, the Turing–Hopf–Turing bifurcation occurs, and we also find the case about the spatial resonance of Turing–Turing bifurcation arising, and two kinds spatially steady-state solutions are found which are synchronous or anti-phased. Finally, sample numerical results are reported. © Springer Nature B.V. 2019 |
| abstractGer |
Abstract Motivated by the dynamics of neuronal responses, we analyze the dynamics of the FitzHugh–Nagumo slow–fast system with diffusion and coupling. In the case of diffusion, the system provides a canonical example of Turing–Hopf bifurcation. By analyzing the linear stability of the local equilibrium, the occurrence of Turing–Hopf bifurcation, Turing–Turing bifurcation and coupled Turing–Hopf bifurcation are obtained. The normal form associated with the Turing–Hopf bifurcation is obtained by using the procedure of Song for calculating the normal form of PDEs. Further, in the case of two coupled FitzHugh–Nagumo reaction–diffusion, the Turing–Hopf–Turing bifurcation occurs, and we also find the case about the spatial resonance of Turing–Turing bifurcation arising, and two kinds spatially steady-state solutions are found which are synchronous or anti-phased. Finally, sample numerical results are reported. © Springer Nature B.V. 2019 |
| abstract_unstemmed |
Abstract Motivated by the dynamics of neuronal responses, we analyze the dynamics of the FitzHugh–Nagumo slow–fast system with diffusion and coupling. In the case of diffusion, the system provides a canonical example of Turing–Hopf bifurcation. By analyzing the linear stability of the local equilibrium, the occurrence of Turing–Hopf bifurcation, Turing–Turing bifurcation and coupled Turing–Hopf bifurcation are obtained. The normal form associated with the Turing–Hopf bifurcation is obtained by using the procedure of Song for calculating the normal form of PDEs. Further, in the case of two coupled FitzHugh–Nagumo reaction–diffusion, the Turing–Hopf–Turing bifurcation occurs, and we also find the case about the spatial resonance of Turing–Turing bifurcation arising, and two kinds spatially steady-state solutions are found which are synchronous or anti-phased. Finally, sample numerical results are reported. © Springer Nature B.V. 2019 |
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2 |
| title_short |
Patterns of interaction of coupled reaction–diffusion systems of the FitzHugh–Nagumo type |
| url |
https://doi.org/10.1007/s11071-019-05065-8 |
| remote_bool |
false |
| author2 |
Ke, Ai Zheng, Baodong |
| author2Str |
Ke, Ai Zheng, Baodong |
| ppnlink |
130936782 |
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| hochschulschrift_bool |
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| doi_str |
10.1007/s11071-019-05065-8 |
| up_date |
2024-07-04T03:40:25.566Z |
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