A reaction diffusion model for understanding phyllotactic formation
Abstract Phyllotactic patterns in plants are well known to be related to the golden ratio. Actually, many mathematical models using the theoretical inhibitory effect were proposed to reproduce these phyllotactic patterns. In 1996, Douady and Couder introduced a model using magnetic repulsion and suc...
Ausführliche Beschreibung
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| Autor*in: |
Tanaka, Yoshitaro [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015 |
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| Schlagwörter: |
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| Anmerkung: |
© The JJIAM Publishing Committee and Springer Japan 2015 |
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| Übergeordnetes Werk: |
Enthalten in: Japan journal of industrial and applied mathematics - London : Springer Nature, 1991, 33(2015), 1 vom: 25. Nov., Seite 183-205 |
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| Übergeordnetes Werk: |
volume:33 ; year:2015 ; number:1 ; day:25 ; month:11 ; pages:183-205 |
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| DOI / URN: |
10.1007/s13160-015-0202-8 |
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SPR030707781 |
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| 245 | 1 | 2 | |a A reaction diffusion model for understanding phyllotactic formation |
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| 520 | |a Abstract Phyllotactic patterns in plants are well known to be related to the golden ratio. Actually, many mathematical models using the theoretical inhibitory effect were proposed to reproduce these phyllotactic patterns. In 1996, Douady and Couder introduced a model using magnetic repulsion and succeeded in reproducing phyllotactic patterns numerically. On the other hand, it was recently revealed in biological experiments that a plant hormone, auxin, regulates the phyllotactic formation as an activator (Reinhardt et al., Nature 426:255–260, 2003). Then, there arises a natural question as to how the inhibitory effect can be related to the auxin. In this paper, a reaction diffusion model is proposed by taking account of auxin behavior in plant tips. The relationship between Douady and Couder’s model and our model is shown by singular limit analysis. It also provides us with the potential function corresponding to the inhibitory effect, and the bifurcation diagram. | ||
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| 650 | 4 | |a Reaction diffusion model |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Singular limit analysis |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Mimura, Masayasu |4 aut | |
| 700 | 1 | |a Ninomiya, Hirokazu |4 aut | |
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10.1007/s13160-015-0202-8 doi (DE-627)SPR030707781 (SPR)s13160-015-0202-8-e DE-627 ger DE-627 rakwb eng Tanaka, Yoshitaro verfasserin aut A reaction diffusion model for understanding phyllotactic formation 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The JJIAM Publishing Committee and Springer Japan 2015 Abstract Phyllotactic patterns in plants are well known to be related to the golden ratio. Actually, many mathematical models using the theoretical inhibitory effect were proposed to reproduce these phyllotactic patterns. In 1996, Douady and Couder introduced a model using magnetic repulsion and succeeded in reproducing phyllotactic patterns numerically. On the other hand, it was recently revealed in biological experiments that a plant hormone, auxin, regulates the phyllotactic formation as an activator (Reinhardt et al., Nature 426:255–260, 2003). Then, there arises a natural question as to how the inhibitory effect can be related to the auxin. In this paper, a reaction diffusion model is proposed by taking account of auxin behavior in plant tips. The relationship between Douady and Couder’s model and our model is shown by singular limit analysis. It also provides us with the potential function corresponding to the inhibitory effect, and the bifurcation diagram. Phyllotaxis (dpeaa)DE-He213 Golden ratio (dpeaa)DE-He213 Basipetal transport (dpeaa)DE-He213 Reaction diffusion model (dpeaa)DE-He213 Singular limit analysis (dpeaa)DE-He213 Mimura, Masayasu aut Ninomiya, Hirokazu aut Enthalten in Japan journal of industrial and applied mathematics London : Springer Nature, 1991 33(2015), 1 vom: 25. Nov., Seite 183-205 (DE-627)566010836 (DE-600)2425253-0 1868-937X nnns volume:33 year:2015 number:1 day:25 month:11 pages:183-205 https://dx.doi.org/10.1007/s13160-015-0202-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 33 2015 1 25 11 183-205 |
| spelling |
10.1007/s13160-015-0202-8 doi (DE-627)SPR030707781 (SPR)s13160-015-0202-8-e DE-627 ger DE-627 rakwb eng Tanaka, Yoshitaro verfasserin aut A reaction diffusion model for understanding phyllotactic formation 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The JJIAM Publishing Committee and Springer Japan 2015 Abstract Phyllotactic patterns in plants are well known to be related to the golden ratio. Actually, many mathematical models using the theoretical inhibitory effect were proposed to reproduce these phyllotactic patterns. In 1996, Douady and Couder introduced a model using magnetic repulsion and succeeded in reproducing phyllotactic patterns numerically. On the other hand, it was recently revealed in biological experiments that a plant hormone, auxin, regulates the phyllotactic formation as an activator (Reinhardt et al., Nature 426:255–260, 2003). Then, there arises a natural question as to how the inhibitory effect can be related to the auxin. In this paper, a reaction diffusion model is proposed by taking account of auxin behavior in plant tips. The relationship between Douady and Couder’s model and our model is shown by singular limit analysis. It also provides us with the potential function corresponding to the inhibitory effect, and the bifurcation diagram. Phyllotaxis (dpeaa)DE-He213 Golden ratio (dpeaa)DE-He213 Basipetal transport (dpeaa)DE-He213 Reaction diffusion model (dpeaa)DE-He213 Singular limit analysis (dpeaa)DE-He213 Mimura, Masayasu aut Ninomiya, Hirokazu aut Enthalten in Japan journal of industrial and applied mathematics London : Springer Nature, 1991 33(2015), 1 vom: 25. Nov., Seite 183-205 (DE-627)566010836 (DE-600)2425253-0 1868-937X nnns volume:33 year:2015 number:1 day:25 month:11 pages:183-205 https://dx.doi.org/10.1007/s13160-015-0202-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 33 2015 1 25 11 183-205 |
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10.1007/s13160-015-0202-8 doi (DE-627)SPR030707781 (SPR)s13160-015-0202-8-e DE-627 ger DE-627 rakwb eng Tanaka, Yoshitaro verfasserin aut A reaction diffusion model for understanding phyllotactic formation 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The JJIAM Publishing Committee and Springer Japan 2015 Abstract Phyllotactic patterns in plants are well known to be related to the golden ratio. Actually, many mathematical models using the theoretical inhibitory effect were proposed to reproduce these phyllotactic patterns. In 1996, Douady and Couder introduced a model using magnetic repulsion and succeeded in reproducing phyllotactic patterns numerically. On the other hand, it was recently revealed in biological experiments that a plant hormone, auxin, regulates the phyllotactic formation as an activator (Reinhardt et al., Nature 426:255–260, 2003). Then, there arises a natural question as to how the inhibitory effect can be related to the auxin. In this paper, a reaction diffusion model is proposed by taking account of auxin behavior in plant tips. The relationship between Douady and Couder’s model and our model is shown by singular limit analysis. It also provides us with the potential function corresponding to the inhibitory effect, and the bifurcation diagram. Phyllotaxis (dpeaa)DE-He213 Golden ratio (dpeaa)DE-He213 Basipetal transport (dpeaa)DE-He213 Reaction diffusion model (dpeaa)DE-He213 Singular limit analysis (dpeaa)DE-He213 Mimura, Masayasu aut Ninomiya, Hirokazu aut Enthalten in Japan journal of industrial and applied mathematics London : Springer Nature, 1991 33(2015), 1 vom: 25. Nov., Seite 183-205 (DE-627)566010836 (DE-600)2425253-0 1868-937X nnns volume:33 year:2015 number:1 day:25 month:11 pages:183-205 https://dx.doi.org/10.1007/s13160-015-0202-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 33 2015 1 25 11 183-205 |
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10.1007/s13160-015-0202-8 doi (DE-627)SPR030707781 (SPR)s13160-015-0202-8-e DE-627 ger DE-627 rakwb eng Tanaka, Yoshitaro verfasserin aut A reaction diffusion model for understanding phyllotactic formation 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The JJIAM Publishing Committee and Springer Japan 2015 Abstract Phyllotactic patterns in plants are well known to be related to the golden ratio. Actually, many mathematical models using the theoretical inhibitory effect were proposed to reproduce these phyllotactic patterns. In 1996, Douady and Couder introduced a model using magnetic repulsion and succeeded in reproducing phyllotactic patterns numerically. On the other hand, it was recently revealed in biological experiments that a plant hormone, auxin, regulates the phyllotactic formation as an activator (Reinhardt et al., Nature 426:255–260, 2003). Then, there arises a natural question as to how the inhibitory effect can be related to the auxin. In this paper, a reaction diffusion model is proposed by taking account of auxin behavior in plant tips. The relationship between Douady and Couder’s model and our model is shown by singular limit analysis. It also provides us with the potential function corresponding to the inhibitory effect, and the bifurcation diagram. Phyllotaxis (dpeaa)DE-He213 Golden ratio (dpeaa)DE-He213 Basipetal transport (dpeaa)DE-He213 Reaction diffusion model (dpeaa)DE-He213 Singular limit analysis (dpeaa)DE-He213 Mimura, Masayasu aut Ninomiya, Hirokazu aut Enthalten in Japan journal of industrial and applied mathematics London : Springer Nature, 1991 33(2015), 1 vom: 25. Nov., Seite 183-205 (DE-627)566010836 (DE-600)2425253-0 1868-937X nnns volume:33 year:2015 number:1 day:25 month:11 pages:183-205 https://dx.doi.org/10.1007/s13160-015-0202-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 33 2015 1 25 11 183-205 |
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10.1007/s13160-015-0202-8 doi (DE-627)SPR030707781 (SPR)s13160-015-0202-8-e DE-627 ger DE-627 rakwb eng Tanaka, Yoshitaro verfasserin aut A reaction diffusion model for understanding phyllotactic formation 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The JJIAM Publishing Committee and Springer Japan 2015 Abstract Phyllotactic patterns in plants are well known to be related to the golden ratio. Actually, many mathematical models using the theoretical inhibitory effect were proposed to reproduce these phyllotactic patterns. In 1996, Douady and Couder introduced a model using magnetic repulsion and succeeded in reproducing phyllotactic patterns numerically. On the other hand, it was recently revealed in biological experiments that a plant hormone, auxin, regulates the phyllotactic formation as an activator (Reinhardt et al., Nature 426:255–260, 2003). Then, there arises a natural question as to how the inhibitory effect can be related to the auxin. In this paper, a reaction diffusion model is proposed by taking account of auxin behavior in plant tips. The relationship between Douady and Couder’s model and our model is shown by singular limit analysis. It also provides us with the potential function corresponding to the inhibitory effect, and the bifurcation diagram. Phyllotaxis (dpeaa)DE-He213 Golden ratio (dpeaa)DE-He213 Basipetal transport (dpeaa)DE-He213 Reaction diffusion model (dpeaa)DE-He213 Singular limit analysis (dpeaa)DE-He213 Mimura, Masayasu aut Ninomiya, Hirokazu aut Enthalten in Japan journal of industrial and applied mathematics London : Springer Nature, 1991 33(2015), 1 vom: 25. Nov., Seite 183-205 (DE-627)566010836 (DE-600)2425253-0 1868-937X nnns volume:33 year:2015 number:1 day:25 month:11 pages:183-205 https://dx.doi.org/10.1007/s13160-015-0202-8 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 33 2015 1 25 11 183-205 |
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Tanaka, Yoshitaro @@aut@@ Mimura, Masayasu @@aut@@ Ninomiya, Hirokazu @@aut@@ |
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Tanaka, Yoshitaro |
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Tanaka, Yoshitaro misc Phyllotaxis misc Golden ratio misc Basipetal transport misc Reaction diffusion model misc Singular limit analysis A reaction diffusion model for understanding phyllotactic formation |
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A reaction diffusion model for understanding phyllotactic formation Phyllotaxis (dpeaa)DE-He213 Golden ratio (dpeaa)DE-He213 Basipetal transport (dpeaa)DE-He213 Reaction diffusion model (dpeaa)DE-He213 Singular limit analysis (dpeaa)DE-He213 |
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reaction diffusion model for understanding phyllotactic formation |
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A reaction diffusion model for understanding phyllotactic formation |
| abstract |
Abstract Phyllotactic patterns in plants are well known to be related to the golden ratio. Actually, many mathematical models using the theoretical inhibitory effect were proposed to reproduce these phyllotactic patterns. In 1996, Douady and Couder introduced a model using magnetic repulsion and succeeded in reproducing phyllotactic patterns numerically. On the other hand, it was recently revealed in biological experiments that a plant hormone, auxin, regulates the phyllotactic formation as an activator (Reinhardt et al., Nature 426:255–260, 2003). Then, there arises a natural question as to how the inhibitory effect can be related to the auxin. In this paper, a reaction diffusion model is proposed by taking account of auxin behavior in plant tips. The relationship between Douady and Couder’s model and our model is shown by singular limit analysis. It also provides us with the potential function corresponding to the inhibitory effect, and the bifurcation diagram. © The JJIAM Publishing Committee and Springer Japan 2015 |
| abstractGer |
Abstract Phyllotactic patterns in plants are well known to be related to the golden ratio. Actually, many mathematical models using the theoretical inhibitory effect were proposed to reproduce these phyllotactic patterns. In 1996, Douady and Couder introduced a model using magnetic repulsion and succeeded in reproducing phyllotactic patterns numerically. On the other hand, it was recently revealed in biological experiments that a plant hormone, auxin, regulates the phyllotactic formation as an activator (Reinhardt et al., Nature 426:255–260, 2003). Then, there arises a natural question as to how the inhibitory effect can be related to the auxin. In this paper, a reaction diffusion model is proposed by taking account of auxin behavior in plant tips. The relationship between Douady and Couder’s model and our model is shown by singular limit analysis. It also provides us with the potential function corresponding to the inhibitory effect, and the bifurcation diagram. © The JJIAM Publishing Committee and Springer Japan 2015 |
| abstract_unstemmed |
Abstract Phyllotactic patterns in plants are well known to be related to the golden ratio. Actually, many mathematical models using the theoretical inhibitory effect were proposed to reproduce these phyllotactic patterns. In 1996, Douady and Couder introduced a model using magnetic repulsion and succeeded in reproducing phyllotactic patterns numerically. On the other hand, it was recently revealed in biological experiments that a plant hormone, auxin, regulates the phyllotactic formation as an activator (Reinhardt et al., Nature 426:255–260, 2003). Then, there arises a natural question as to how the inhibitory effect can be related to the auxin. In this paper, a reaction diffusion model is proposed by taking account of auxin behavior in plant tips. The relationship between Douady and Couder’s model and our model is shown by singular limit analysis. It also provides us with the potential function corresponding to the inhibitory effect, and the bifurcation diagram. © The JJIAM Publishing Committee and Springer Japan 2015 |
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A reaction diffusion model for understanding phyllotactic formation |
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Mimura, Masayasu Ninomiya, Hirokazu |
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