Chapter 8.1 Reaction-Diffusion Models of Pattern Formation in Developmental Biology
In this paper we present mathematical approaches to understand a symmetry break and formation of spatially heterogenous structures during development. We focus on the models given by reaction-diffusion equations and approach the question of possible mechanisms of development of spatially heterogeneo...
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| Autor*in: |
Marciniak-Czochra, Anna [verfasserIn] Antoniouk, Alexandra V. [herausgeberIn] Melnik, Roderick V. N. [herausgeberIn] |
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| Format: |
E-Book |
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| Sprache: |
Englisch |
| Erschienen: |
Berlin/Boston: De Gruyter ; 2012 |
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| Rechteinformationen: |
Open Access All rights reserved |
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| Schlagwörter: |
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| Umfang: |
1 Online-Ressource |
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| Links: | |
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| ISBN: |
978-3-11-028853-7 978-3-11-027372-4 |
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1836393407 |
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| 520 | |a In this paper we present mathematical approaches to understand a symmetry break and formation of spatially heterogenous structures during development. We focus on the models given by reaction-diffusion equations and approach the question of possible mechanisms of development of spatially heterogeneous structures. We discuss two mechanisms of pattern formation: diffusion-driven instability (Turing instability) and a hysteresis-driven mechanism, and demonstrate their possibilities and constraints in explaining different aspects of structure formation in cell systems. Depending on the type of nonlinearities, we show the existence of Turing patterns, the maxima of which may be of the spike or plateau type, and the existence of transition layer stationary solutions. These concepts are discussed on example of morphogenesis of the fresh water polyp Hydra, which is a model organism in developmental biology | ||
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| 700 | 1 | |a Melnik, Roderick V. N. |e herausgeberin |4 edt | |
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9783110288537 191 978-3-11-028853-7 9783110273724 978-3-11-027372-4 (DE-627)1836393407 (DE-599)KEP06211431X (OCoLC)1371338824 (OAPEN)23720 (EBP)06211431X DE-627 eng DE-627 rda eng KNDR bicssc PBKS bicssc PBW bicssc PSA bicssc Marciniak-Czochra, Anna verfasserin aut Chapter 8.1 Reaction-Diffusion Models of Pattern Formation in Developmental Biology Berlin/Boston De Gruyter 2012 1 Online-Ressource Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Open Access Unrestricted online access star In this paper we present mathematical approaches to understand a symmetry break and formation of spatially heterogenous structures during development. We focus on the models given by reaction-diffusion equations and approach the question of possible mechanisms of development of spatially heterogeneous structures. We discuss two mechanisms of pattern formation: diffusion-driven instability (Turing instability) and a hysteresis-driven mechanism, and demonstrate their possibilities and constraints in explaining different aspects of structure formation in cell systems. Depending on the type of nonlinearities, we show the existence of Turing patterns, the maxima of which may be of the spike or plateau type, and the existence of transition layer stationary solutions. These concepts are discussed on example of morphogenesis of the fresh water polyp Hydra, which is a model organism in developmental biology All rights reserved English Road vehicle manufacturing industry Numerical analysis Applied mathematics Life sciences: general issues Vehicle and transport manufacturing industries Antoniouk, Alexandra V. herausgeberin edt Melnik, Roderick V. N. herausgeberin edt https://library.oapen.org/bitstream/id/f5373516-cab2-4d42-a857-0ff5f8c10d2f/6_[9783110288537 - Mathematics] 8.1 Reaction-Diffusion.pdf X:OAPEN Verlag OAPEN Library: download the publication kostenfrei http://library.oapen.org/handle/20.500.12657/23720 X:OAPEN Verlag OAPEN Library: description of the publication kostenfrei ZDB-94-OAL GBV_ILN_22 ISIL_DE-18 SYSFLAG_1 GBV_KXP GBV_ILN_23 ISIL_DE-830 GBV_ILN_30 ISIL_DE-104 GBV_ILN_31 ISIL_DE-27 GBV_ILN_34 ISIL_DE-18-302 GBV_ILN_39 ISIL_DE-547 GBV_ILN_40 ISIL_DE-7 GBV_ILN_63 ISIL_DE-Wim2 GBV_ILN_65 ISIL_DE-3 GBV_ILN_70 ISIL_DE-89 GBV_ILN_72 ISIL_DE-35 GBV_ILN_95 ISIL_DE-542 GBV_ILN_110 ISIL_DE-Luen4 GBV_ILN_136 ISIL_DE-Wis1 GBV_ILN_147 ISIL_DE-Fl3 GBV_ILN_161 ISIL_DE-960 GBV_ILN_187 ISIL_DE-Ki95 GBV_ILN_213 ISIL_DE-551 GBV_ILN_230 ISIL_DE-552 GBV_ILN_283 ISIL_DE-Ha163 GBV_ILN_293 ISIL_DE-960-3 GBV_ILN_370 ISIL_DE-1373 GBV_ILN_603 ISIL_DE-B1556 GBV_ILN_808 GBV_ILN_2403 ISIL_DE-LFER BO 22 01 0018 4280050066 OLR-ZDB-94-OAL OAPEN Library zu 01-03-23 23 01 0830 4280604282 OLR-OAPEN f z 01-03-23 30 01 0104 4280964076 GBV-OAPEN z 01-03-23 31 01 0027 4280241287 z 01-03-23 34 01 3551 4278802838 OLR-OAPEN zi002 01-03-23 39 01 0547 4281154566 GBV-OAPEN ke 01-03-23 40 01 0007 4279871337 OLR-OAPEN xsn 01-03-23 63 01 3401 4281534466 E-Books LF GBV-OAPEN z 01-03-23 65 01 0003 4281758933 OLR-OAPEN z 01-03-23 70 01 0089 428042537X OLR-OAPEN-OA OAPEN Online Library Open Access eBook z 01-03-23 72 01 0035 4278621574 OLR-OAPEN-OA OAPEN Online Library Open Access eBook z 01-03-23 95 01 3095 4343150100 OLR-OAL Vervielfältigungen (z.B. 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Die Weitergabe an Dritte sowie systematisches Downloaden sind untersagt. z 01-03-23 161 01 0960 4278058942 OLR-OAPEN OAPEN Online Library Open Access eBook z 28-02-23 187 01 3520 4278438494 JSTOR Open Access eBook z 28-02-23 213 01 0551 4279158010 OLR-OAPEN OAPEN Online Library Open Access eBook z 01-03-23 230 01 0552 4279335192 OLR-OAPEN OAPEN Online Library Open Access eBook z 01-03-23 283 01 3283 4279694109 OLR-OAL z 01-03-23 293 01 3293 4278238223 OLR-OAPEN OAPEN Online Library Open Access eBook z 28-02-23 370 01 4370 4278980574 OLR-FREE Kostenloser Zugriff z 01-03-23 603 01 4603 4277881157 OLR-OAPEN Bitte beachten Sie die Nutzungsbedingungen und Copyright-Bestimmungen des Verlages/Herausgebers. z 28-02-23 808 01 4808 428078311X OLR-OAPEN OAPEN Library zg 01-03-23 2403 01 DE-LFER 4307153367 00 --%%-- --%%-- n --%%-- l01 10-04-23 22 01 0018 Volltextzugang http://library.oapen.org/handle/20.500.12657/23720 23 01 0830 http://library.oapen.org/handle/20.500.12657/23720 30 01 0104 Open Access http://library.oapen.org/handle/20.500.12657/23720 31 01 0027 eBook GBV-OAPEN http://library.oapen.org/handle/20.500.12657/23720 34 01 3551 OpenAccess http://library.oapen.org/handle/20.500.12657/23720 40 01 0007 Volltext, Open Access http://library.oapen.org/handle/20.500.12657/23720 63 01 3401 E-Book http://library.oapen.org/handle/20.500.12657/23720 65 01 0003 Open Access http://library.oapen.org/handle/20.500.12657/23720 65 01 0003 Dieser Titel ist Teil einer Datenbank http://www.bibliothek.uni-regensburg.de/dbinfo/detail.php?titel_id=10728&bib_id=ulb_hal 70 01 0089 http://library.oapen.org/handle/20.500.12657/23720 LF 72 01 0035 http://library.oapen.org/handle/20.500.12657/23720 95 01 3095 http://library.oapen.org/handle/20.500.12657/23720 110 01 3110 Open Access http://library.oapen.org/handle/20.500.12657/23720 136 01 3526 Open Access http://library.oapen.org/handle/20.500.12657/23720 147 01 3528 http://library.oapen.org/handle/20.500.12657/23720 161 01 0960 http://library.oapen.org/handle/20.500.12657/23720 LF 187 01 3520 http://library.oapen.org/handle/20.500.12657/23720 213 01 0551 http://library.oapen.org/handle/20.500.12657/23720 230 01 0552 http://library.oapen.org/handle/20.500.12657/23720 283 01 3283 http://library.oapen.org/handle/20.500.12657/23720 293 01 3293 http://library.oapen.org/handle/20.500.12657/23720 LF 370 01 4370 http://library.oapen.org/handle/20.500.12657/23720 603 01 4603 http://library.oapen.org/handle/20.500.12657/23720 808 01 4808 Volltextzugang http://library.oapen.org/handle/20.500.12657/23720 2403 01 DE-LFER https://library.oapen.org/bitstream/id/f5373516-cab2-4d42-a857-0ff5f8c10d2f/6_[9783110288537 - Mathematics] 8.1 Reaction-Diffusion.pdf 31 01 0027 00 eBook GBV-OAPEN 22 01 0018 OLR-ZDB-94-OAL 23 01 0830 OLR-OAPEN 30 01 0104 GBV-OAPEN 34 01 3551 OLR-OAPEN 39 01 0547 GBV-OAPEN 39 01 0547 LF 40 01 0007 OLR-OAPEN 63 01 3401 E-Books LF GBV-OAPEN 65 01 0003 OLR-OAPEN 70 01 0089 OLR-OAPEN-OA 72 01 0035 OLR-OAPEN-OA 95 01 3095 OLR-OAL 110 01 3110 OLR-GBV-OAPEN 136 01 3526 OLR-OAPEN 147 01 3528 OLR-OAPEN 161 01 0960 OLR-OAPEN 213 01 0551 OLR-OAPEN 230 01 0552 OLR-OAPEN 283 01 3283 OLR-OAL 293 01 3293 OLR-OAPEN 370 01 4370 OLR-FREE 370 01 4370 olr-ebook GBV-OAPEN 603 01 4603 OLR-OAPEN 808 01 4808 OLR-OAPEN |
| spelling |
9783110288537 191 978-3-11-028853-7 9783110273724 978-3-11-027372-4 (DE-627)1836393407 (DE-599)KEP06211431X (OCoLC)1371338824 (OAPEN)23720 (EBP)06211431X DE-627 eng DE-627 rda eng KNDR bicssc PBKS bicssc PBW bicssc PSA bicssc Marciniak-Czochra, Anna verfasserin aut Chapter 8.1 Reaction-Diffusion Models of Pattern Formation in Developmental Biology Berlin/Boston De Gruyter 2012 1 Online-Ressource Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Open Access Unrestricted online access star In this paper we present mathematical approaches to understand a symmetry break and formation of spatially heterogenous structures during development. We focus on the models given by reaction-diffusion equations and approach the question of possible mechanisms of development of spatially heterogeneous structures. We discuss two mechanisms of pattern formation: diffusion-driven instability (Turing instability) and a hysteresis-driven mechanism, and demonstrate their possibilities and constraints in explaining different aspects of structure formation in cell systems. Depending on the type of nonlinearities, we show the existence of Turing patterns, the maxima of which may be of the spike or plateau type, and the existence of transition layer stationary solutions. These concepts are discussed on example of morphogenesis of the fresh water polyp Hydra, which is a model organism in developmental biology All rights reserved English Road vehicle manufacturing industry Numerical analysis Applied mathematics Life sciences: general issues Vehicle and transport manufacturing industries Antoniouk, Alexandra V. herausgeberin edt Melnik, Roderick V. N. herausgeberin edt https://library.oapen.org/bitstream/id/f5373516-cab2-4d42-a857-0ff5f8c10d2f/6_[9783110288537 - Mathematics] 8.1 Reaction-Diffusion.pdf X:OAPEN Verlag OAPEN Library: download the publication kostenfrei http://library.oapen.org/handle/20.500.12657/23720 X:OAPEN Verlag OAPEN Library: description of the publication kostenfrei ZDB-94-OAL GBV_ILN_22 ISIL_DE-18 SYSFLAG_1 GBV_KXP GBV_ILN_23 ISIL_DE-830 GBV_ILN_30 ISIL_DE-104 GBV_ILN_31 ISIL_DE-27 GBV_ILN_34 ISIL_DE-18-302 GBV_ILN_39 ISIL_DE-547 GBV_ILN_40 ISIL_DE-7 GBV_ILN_63 ISIL_DE-Wim2 GBV_ILN_65 ISIL_DE-3 GBV_ILN_70 ISIL_DE-89 GBV_ILN_72 ISIL_DE-35 GBV_ILN_95 ISIL_DE-542 GBV_ILN_110 ISIL_DE-Luen4 GBV_ILN_136 ISIL_DE-Wis1 GBV_ILN_147 ISIL_DE-Fl3 GBV_ILN_161 ISIL_DE-960 GBV_ILN_187 ISIL_DE-Ki95 GBV_ILN_213 ISIL_DE-551 GBV_ILN_230 ISIL_DE-552 GBV_ILN_283 ISIL_DE-Ha163 GBV_ILN_293 ISIL_DE-960-3 GBV_ILN_370 ISIL_DE-1373 GBV_ILN_603 ISIL_DE-B1556 GBV_ILN_808 GBV_ILN_2403 ISIL_DE-LFER BO 22 01 0018 4280050066 OLR-ZDB-94-OAL OAPEN Library zu 01-03-23 23 01 0830 4280604282 OLR-OAPEN f z 01-03-23 30 01 0104 4280964076 GBV-OAPEN z 01-03-23 31 01 0027 4280241287 z 01-03-23 34 01 3551 4278802838 OLR-OAPEN zi002 01-03-23 39 01 0547 4281154566 GBV-OAPEN ke 01-03-23 40 01 0007 4279871337 OLR-OAPEN xsn 01-03-23 63 01 3401 4281534466 E-Books LF GBV-OAPEN z 01-03-23 65 01 0003 4281758933 OLR-OAPEN z 01-03-23 70 01 0089 428042537X OLR-OAPEN-OA OAPEN Online Library Open Access eBook z 01-03-23 72 01 0035 4278621574 OLR-OAPEN-OA OAPEN Online Library Open Access eBook z 01-03-23 95 01 3095 4343150100 OLR-OAL Vervielfältigungen (z.B. Kopien, Downloads) sind nur von einzelnen Kapiteln oder Seiten und nur zum eigenen wissenschaftlichen Gebrauch erlaubt. Die Weitergabe an Dritte sowie systematisches Downloaden sind untersagt. z 24-06-23 110 01 3110 4281339299 OLR-GBV-OAPEN Open Access z 01-03-23 136 01 3526 427951240X OLR-OAPEN z 01-03-23 147 01 3528 4281981578 OLR-OAPEN frei verfügbar für Europa-Universität Flensburg, Hochschule Flensburg und Zentrale Hochschulbibliothek Vervielfältigungen (z.B. Kopien, Downloads) sind nur von einzelnen Kapiteln oder Seiten und nur zum eigenen wissenschaftlichen Gebrauch erlaubt. Die Weitergabe an Dritte sowie systematisches Downloaden sind untersagt. z 01-03-23 161 01 0960 4278058942 OLR-OAPEN OAPEN Online Library Open Access eBook z 28-02-23 187 01 3520 4278438494 JSTOR Open Access eBook z 28-02-23 213 01 0551 4279158010 OLR-OAPEN OAPEN Online Library Open Access eBook z 01-03-23 230 01 0552 4279335192 OLR-OAPEN OAPEN Online Library Open Access eBook z 01-03-23 283 01 3283 4279694109 OLR-OAL z 01-03-23 293 01 3293 4278238223 OLR-OAPEN OAPEN Online Library Open Access eBook z 28-02-23 370 01 4370 4278980574 OLR-FREE Kostenloser Zugriff z 01-03-23 603 01 4603 4277881157 OLR-OAPEN Bitte beachten Sie die Nutzungsbedingungen und Copyright-Bestimmungen des Verlages/Herausgebers. z 28-02-23 808 01 4808 428078311X OLR-OAPEN OAPEN Library zg 01-03-23 2403 01 DE-LFER 4307153367 00 --%%-- --%%-- n --%%-- l01 10-04-23 22 01 0018 Volltextzugang http://library.oapen.org/handle/20.500.12657/23720 23 01 0830 http://library.oapen.org/handle/20.500.12657/23720 30 01 0104 Open Access http://library.oapen.org/handle/20.500.12657/23720 31 01 0027 eBook GBV-OAPEN http://library.oapen.org/handle/20.500.12657/23720 34 01 3551 OpenAccess http://library.oapen.org/handle/20.500.12657/23720 40 01 0007 Volltext, Open Access http://library.oapen.org/handle/20.500.12657/23720 63 01 3401 E-Book http://library.oapen.org/handle/20.500.12657/23720 65 01 0003 Open Access http://library.oapen.org/handle/20.500.12657/23720 65 01 0003 Dieser Titel ist Teil einer Datenbank http://www.bibliothek.uni-regensburg.de/dbinfo/detail.php?titel_id=10728&bib_id=ulb_hal 70 01 0089 http://library.oapen.org/handle/20.500.12657/23720 LF 72 01 0035 http://library.oapen.org/handle/20.500.12657/23720 95 01 3095 http://library.oapen.org/handle/20.500.12657/23720 110 01 3110 Open Access http://library.oapen.org/handle/20.500.12657/23720 136 01 3526 Open Access http://library.oapen.org/handle/20.500.12657/23720 147 01 3528 http://library.oapen.org/handle/20.500.12657/23720 161 01 0960 http://library.oapen.org/handle/20.500.12657/23720 LF 187 01 3520 http://library.oapen.org/handle/20.500.12657/23720 213 01 0551 http://library.oapen.org/handle/20.500.12657/23720 230 01 0552 http://library.oapen.org/handle/20.500.12657/23720 283 01 3283 http://library.oapen.org/handle/20.500.12657/23720 293 01 3293 http://library.oapen.org/handle/20.500.12657/23720 LF 370 01 4370 http://library.oapen.org/handle/20.500.12657/23720 603 01 4603 http://library.oapen.org/handle/20.500.12657/23720 808 01 4808 Volltextzugang http://library.oapen.org/handle/20.500.12657/23720 2403 01 DE-LFER https://library.oapen.org/bitstream/id/f5373516-cab2-4d42-a857-0ff5f8c10d2f/6_[9783110288537 - Mathematics] 8.1 Reaction-Diffusion.pdf 31 01 0027 00 eBook GBV-OAPEN 22 01 0018 OLR-ZDB-94-OAL 23 01 0830 OLR-OAPEN 30 01 0104 GBV-OAPEN 34 01 3551 OLR-OAPEN 39 01 0547 GBV-OAPEN 39 01 0547 LF 40 01 0007 OLR-OAPEN 63 01 3401 E-Books LF GBV-OAPEN 65 01 0003 OLR-OAPEN 70 01 0089 OLR-OAPEN-OA 72 01 0035 OLR-OAPEN-OA 95 01 3095 OLR-OAL 110 01 3110 OLR-GBV-OAPEN 136 01 3526 OLR-OAPEN 147 01 3528 OLR-OAPEN 161 01 0960 OLR-OAPEN 213 01 0551 OLR-OAPEN 230 01 0552 OLR-OAPEN 283 01 3283 OLR-OAL 293 01 3293 OLR-OAPEN 370 01 4370 OLR-FREE 370 01 4370 olr-ebook GBV-OAPEN 603 01 4603 OLR-OAPEN 808 01 4808 OLR-OAPEN |
| allfields_unstemmed |
9783110288537 191 978-3-11-028853-7 9783110273724 978-3-11-027372-4 (DE-627)1836393407 (DE-599)KEP06211431X (OCoLC)1371338824 (OAPEN)23720 (EBP)06211431X DE-627 eng DE-627 rda eng KNDR bicssc PBKS bicssc PBW bicssc PSA bicssc Marciniak-Czochra, Anna verfasserin aut Chapter 8.1 Reaction-Diffusion Models of Pattern Formation in Developmental Biology Berlin/Boston De Gruyter 2012 1 Online-Ressource Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Open Access Unrestricted online access star In this paper we present mathematical approaches to understand a symmetry break and formation of spatially heterogenous structures during development. We focus on the models given by reaction-diffusion equations and approach the question of possible mechanisms of development of spatially heterogeneous structures. We discuss two mechanisms of pattern formation: diffusion-driven instability (Turing instability) and a hysteresis-driven mechanism, and demonstrate their possibilities and constraints in explaining different aspects of structure formation in cell systems. Depending on the type of nonlinearities, we show the existence of Turing patterns, the maxima of which may be of the spike or plateau type, and the existence of transition layer stationary solutions. These concepts are discussed on example of morphogenesis of the fresh water polyp Hydra, which is a model organism in developmental biology All rights reserved English Road vehicle manufacturing industry Numerical analysis Applied mathematics Life sciences: general issues Vehicle and transport manufacturing industries Antoniouk, Alexandra V. herausgeberin edt Melnik, Roderick V. N. herausgeberin edt https://library.oapen.org/bitstream/id/f5373516-cab2-4d42-a857-0ff5f8c10d2f/6_[9783110288537 - Mathematics] 8.1 Reaction-Diffusion.pdf X:OAPEN Verlag OAPEN Library: download the publication kostenfrei http://library.oapen.org/handle/20.500.12657/23720 X:OAPEN Verlag OAPEN Library: description of the publication kostenfrei ZDB-94-OAL GBV_ILN_22 ISIL_DE-18 SYSFLAG_1 GBV_KXP GBV_ILN_23 ISIL_DE-830 GBV_ILN_30 ISIL_DE-104 GBV_ILN_31 ISIL_DE-27 GBV_ILN_34 ISIL_DE-18-302 GBV_ILN_39 ISIL_DE-547 GBV_ILN_40 ISIL_DE-7 GBV_ILN_63 ISIL_DE-Wim2 GBV_ILN_65 ISIL_DE-3 GBV_ILN_70 ISIL_DE-89 GBV_ILN_72 ISIL_DE-35 GBV_ILN_95 ISIL_DE-542 GBV_ILN_110 ISIL_DE-Luen4 GBV_ILN_136 ISIL_DE-Wis1 GBV_ILN_147 ISIL_DE-Fl3 GBV_ILN_161 ISIL_DE-960 GBV_ILN_187 ISIL_DE-Ki95 GBV_ILN_213 ISIL_DE-551 GBV_ILN_230 ISIL_DE-552 GBV_ILN_283 ISIL_DE-Ha163 GBV_ILN_293 ISIL_DE-960-3 GBV_ILN_370 ISIL_DE-1373 GBV_ILN_603 ISIL_DE-B1556 GBV_ILN_808 GBV_ILN_2403 ISIL_DE-LFER BO 22 01 0018 4280050066 OLR-ZDB-94-OAL OAPEN Library zu 01-03-23 23 01 0830 4280604282 OLR-OAPEN f z 01-03-23 30 01 0104 4280964076 GBV-OAPEN z 01-03-23 31 01 0027 4280241287 z 01-03-23 34 01 3551 4278802838 OLR-OAPEN zi002 01-03-23 39 01 0547 4281154566 GBV-OAPEN ke 01-03-23 40 01 0007 4279871337 OLR-OAPEN xsn 01-03-23 63 01 3401 4281534466 E-Books LF GBV-OAPEN z 01-03-23 65 01 0003 4281758933 OLR-OAPEN z 01-03-23 70 01 0089 428042537X OLR-OAPEN-OA OAPEN Online Library Open Access eBook z 01-03-23 72 01 0035 4278621574 OLR-OAPEN-OA OAPEN Online Library Open Access eBook z 01-03-23 95 01 3095 4343150100 OLR-OAL Vervielfältigungen (z.B. Kopien, Downloads) sind nur von einzelnen Kapiteln oder Seiten und nur zum eigenen wissenschaftlichen Gebrauch erlaubt. Die Weitergabe an Dritte sowie systematisches Downloaden sind untersagt. z 24-06-23 110 01 3110 4281339299 OLR-GBV-OAPEN Open Access z 01-03-23 136 01 3526 427951240X OLR-OAPEN z 01-03-23 147 01 3528 4281981578 OLR-OAPEN frei verfügbar für Europa-Universität Flensburg, Hochschule Flensburg und Zentrale Hochschulbibliothek Vervielfältigungen (z.B. Kopien, Downloads) sind nur von einzelnen Kapiteln oder Seiten und nur zum eigenen wissenschaftlichen Gebrauch erlaubt. Die Weitergabe an Dritte sowie systematisches Downloaden sind untersagt. z 01-03-23 161 01 0960 4278058942 OLR-OAPEN OAPEN Online Library Open Access eBook z 28-02-23 187 01 3520 4278438494 JSTOR Open Access eBook z 28-02-23 213 01 0551 4279158010 OLR-OAPEN OAPEN Online Library Open Access eBook z 01-03-23 230 01 0552 4279335192 OLR-OAPEN OAPEN Online Library Open Access eBook z 01-03-23 283 01 3283 4279694109 OLR-OAL z 01-03-23 293 01 3293 4278238223 OLR-OAPEN OAPEN Online Library Open Access eBook z 28-02-23 370 01 4370 4278980574 OLR-FREE Kostenloser Zugriff z 01-03-23 603 01 4603 4277881157 OLR-OAPEN Bitte beachten Sie die Nutzungsbedingungen und Copyright-Bestimmungen des Verlages/Herausgebers. z 28-02-23 808 01 4808 428078311X OLR-OAPEN OAPEN Library zg 01-03-23 2403 01 DE-LFER 4307153367 00 --%%-- --%%-- n --%%-- l01 10-04-23 22 01 0018 Volltextzugang http://library.oapen.org/handle/20.500.12657/23720 23 01 0830 http://library.oapen.org/handle/20.500.12657/23720 30 01 0104 Open Access http://library.oapen.org/handle/20.500.12657/23720 31 01 0027 eBook GBV-OAPEN http://library.oapen.org/handle/20.500.12657/23720 34 01 3551 OpenAccess http://library.oapen.org/handle/20.500.12657/23720 40 01 0007 Volltext, Open Access http://library.oapen.org/handle/20.500.12657/23720 63 01 3401 E-Book http://library.oapen.org/handle/20.500.12657/23720 65 01 0003 Open Access http://library.oapen.org/handle/20.500.12657/23720 65 01 0003 Dieser Titel ist Teil einer Datenbank http://www.bibliothek.uni-regensburg.de/dbinfo/detail.php?titel_id=10728&bib_id=ulb_hal 70 01 0089 http://library.oapen.org/handle/20.500.12657/23720 LF 72 01 0035 http://library.oapen.org/handle/20.500.12657/23720 95 01 3095 http://library.oapen.org/handle/20.500.12657/23720 110 01 3110 Open Access http://library.oapen.org/handle/20.500.12657/23720 136 01 3526 Open Access http://library.oapen.org/handle/20.500.12657/23720 147 01 3528 http://library.oapen.org/handle/20.500.12657/23720 161 01 0960 http://library.oapen.org/handle/20.500.12657/23720 LF 187 01 3520 http://library.oapen.org/handle/20.500.12657/23720 213 01 0551 http://library.oapen.org/handle/20.500.12657/23720 230 01 0552 http://library.oapen.org/handle/20.500.12657/23720 283 01 3283 http://library.oapen.org/handle/20.500.12657/23720 293 01 3293 http://library.oapen.org/handle/20.500.12657/23720 LF 370 01 4370 http://library.oapen.org/handle/20.500.12657/23720 603 01 4603 http://library.oapen.org/handle/20.500.12657/23720 808 01 4808 Volltextzugang http://library.oapen.org/handle/20.500.12657/23720 2403 01 DE-LFER https://library.oapen.org/bitstream/id/f5373516-cab2-4d42-a857-0ff5f8c10d2f/6_[9783110288537 - Mathematics] 8.1 Reaction-Diffusion.pdf 31 01 0027 00 eBook GBV-OAPEN 22 01 0018 OLR-ZDB-94-OAL 23 01 0830 OLR-OAPEN 30 01 0104 GBV-OAPEN 34 01 3551 OLR-OAPEN 39 01 0547 GBV-OAPEN 39 01 0547 LF 40 01 0007 OLR-OAPEN 63 01 3401 E-Books LF GBV-OAPEN 65 01 0003 OLR-OAPEN 70 01 0089 OLR-OAPEN-OA 72 01 0035 OLR-OAPEN-OA 95 01 3095 OLR-OAL 110 01 3110 OLR-GBV-OAPEN 136 01 3526 OLR-OAPEN 147 01 3528 OLR-OAPEN 161 01 0960 OLR-OAPEN 213 01 0551 OLR-OAPEN 230 01 0552 OLR-OAPEN 283 01 3283 OLR-OAL 293 01 3293 OLR-OAPEN 370 01 4370 OLR-FREE 370 01 4370 olr-ebook GBV-OAPEN 603 01 4603 OLR-OAPEN 808 01 4808 OLR-OAPEN |
| allfieldsGer |
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We discuss two mechanisms of pattern formation: diffusion-driven instability (Turing instability) and a hysteresis-driven mechanism, and demonstrate their possibilities and constraints in explaining different aspects of structure formation in cell systems. Depending on the type of nonlinearities, we show the existence of Turing patterns, the maxima of which may be of the spike or plateau type, and the existence of transition layer stationary solutions. These concepts are discussed on example of morphogenesis of the fresh water polyp Hydra, which is a model organism in developmental biology All rights reserved English Road vehicle manufacturing industry Numerical analysis Applied mathematics Life sciences: general issues Vehicle and transport manufacturing industries Antoniouk, Alexandra V. herausgeberin edt Melnik, Roderick V. N. herausgeberin edt https://library.oapen.org/bitstream/id/f5373516-cab2-4d42-a857-0ff5f8c10d2f/6_[9783110288537 - Mathematics] 8.1 Reaction-Diffusion.pdf X:OAPEN Verlag OAPEN Library: download the publication kostenfrei http://library.oapen.org/handle/20.500.12657/23720 X:OAPEN Verlag OAPEN Library: description of the publication kostenfrei ZDB-94-OAL GBV_ILN_22 ISIL_DE-18 SYSFLAG_1 GBV_KXP GBV_ILN_23 ISIL_DE-830 GBV_ILN_30 ISIL_DE-104 GBV_ILN_31 ISIL_DE-27 GBV_ILN_34 ISIL_DE-18-302 GBV_ILN_39 ISIL_DE-547 GBV_ILN_40 ISIL_DE-7 GBV_ILN_63 ISIL_DE-Wim2 GBV_ILN_65 ISIL_DE-3 GBV_ILN_70 ISIL_DE-89 GBV_ILN_72 ISIL_DE-35 GBV_ILN_95 ISIL_DE-542 GBV_ILN_110 ISIL_DE-Luen4 GBV_ILN_136 ISIL_DE-Wis1 GBV_ILN_147 ISIL_DE-Fl3 GBV_ILN_161 ISIL_DE-960 GBV_ILN_187 ISIL_DE-Ki95 GBV_ILN_213 ISIL_DE-551 GBV_ILN_230 ISIL_DE-552 GBV_ILN_283 ISIL_DE-Ha163 GBV_ILN_293 ISIL_DE-960-3 GBV_ILN_370 ISIL_DE-1373 GBV_ILN_603 ISIL_DE-B1556 GBV_ILN_808 GBV_ILN_2403 ISIL_DE-LFER BO 22 01 0018 4280050066 OLR-ZDB-94-OAL OAPEN Library zu 01-03-23 23 01 0830 4280604282 OLR-OAPEN f z 01-03-23 30 01 0104 4280964076 GBV-OAPEN z 01-03-23 31 01 0027 4280241287 z 01-03-23 34 01 3551 4278802838 OLR-OAPEN zi002 01-03-23 39 01 0547 4281154566 GBV-OAPEN ke 01-03-23 40 01 0007 4279871337 OLR-OAPEN xsn 01-03-23 63 01 3401 4281534466 E-Books LF GBV-OAPEN z 01-03-23 65 01 0003 4281758933 OLR-OAPEN z 01-03-23 70 01 0089 428042537X OLR-OAPEN-OA OAPEN Online Library Open Access eBook z 01-03-23 72 01 0035 4278621574 OLR-OAPEN-OA OAPEN Online Library Open Access eBook z 01-03-23 95 01 3095 4343150100 OLR-OAL Vervielfältigungen (z.B. 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N. herausgeberin edt https://library.oapen.org/bitstream/id/f5373516-cab2-4d42-a857-0ff5f8c10d2f/6_[9783110288537 - Mathematics] 8.1 Reaction-Diffusion.pdf X:OAPEN Verlag OAPEN Library: download the publication kostenfrei http://library.oapen.org/handle/20.500.12657/23720 X:OAPEN Verlag OAPEN Library: description of the publication kostenfrei ZDB-94-OAL GBV_ILN_22 ISIL_DE-18 SYSFLAG_1 GBV_KXP GBV_ILN_23 ISIL_DE-830 GBV_ILN_30 ISIL_DE-104 GBV_ILN_31 ISIL_DE-27 GBV_ILN_34 ISIL_DE-18-302 GBV_ILN_39 ISIL_DE-547 GBV_ILN_40 ISIL_DE-7 GBV_ILN_63 ISIL_DE-Wim2 GBV_ILN_65 ISIL_DE-3 GBV_ILN_70 ISIL_DE-89 GBV_ILN_72 ISIL_DE-35 GBV_ILN_95 ISIL_DE-542 GBV_ILN_110 ISIL_DE-Luen4 GBV_ILN_136 ISIL_DE-Wis1 GBV_ILN_147 ISIL_DE-Fl3 GBV_ILN_161 ISIL_DE-960 GBV_ILN_187 ISIL_DE-Ki95 GBV_ILN_213 ISIL_DE-551 GBV_ILN_230 ISIL_DE-552 GBV_ILN_283 ISIL_DE-Ha163 GBV_ILN_293 ISIL_DE-960-3 GBV_ILN_370 ISIL_DE-1373 GBV_ILN_603 ISIL_DE-B1556 GBV_ILN_808 GBV_ILN_2403 ISIL_DE-LFER BO 22 01 0018 4280050066 OLR-ZDB-94-OAL OAPEN Library zu 01-03-23 23 01 0830 4280604282 OLR-OAPEN f z 01-03-23 30 01 0104 4280964076 GBV-OAPEN z 01-03-23 31 01 0027 4280241287 z 01-03-23 34 01 3551 4278802838 OLR-OAPEN zi002 01-03-23 39 01 0547 4281154566 GBV-OAPEN ke 01-03-23 40 01 0007 4279871337 OLR-OAPEN xsn 01-03-23 63 01 3401 4281534466 E-Books LF GBV-OAPEN z 01-03-23 65 01 0003 4281758933 OLR-OAPEN z 01-03-23 70 01 0089 428042537X OLR-OAPEN-OA OAPEN Online Library Open Access eBook z 01-03-23 72 01 0035 4278621574 OLR-OAPEN-OA OAPEN Online Library Open Access eBook z 01-03-23 95 01 3095 4343150100 OLR-OAL Vervielfältigungen (z.B. 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In this paper we present mathematical approaches to understand a symmetry break and formation of spatially heterogenous structures during development. We focus on the models given by reaction-diffusion equations and approach the question of possible mechanisms of development of spatially heterogeneous structures. We discuss two mechanisms of pattern formation: diffusion-driven instability (Turing instability) and a hysteresis-driven mechanism, and demonstrate their possibilities and constraints in explaining different aspects of structure formation in cell systems. Depending on the type of nonlinearities, we show the existence of Turing patterns, the maxima of which may be of the spike or plateau type, and the existence of transition layer stationary solutions. These concepts are discussed on example of morphogenesis of the fresh water polyp Hydra, which is a model organism in developmental biology |
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In this paper we present mathematical approaches to understand a symmetry break and formation of spatially heterogenous structures during development. We focus on the models given by reaction-diffusion equations and approach the question of possible mechanisms of development of spatially heterogeneous structures. We discuss two mechanisms of pattern formation: diffusion-driven instability (Turing instability) and a hysteresis-driven mechanism, and demonstrate their possibilities and constraints in explaining different aspects of structure formation in cell systems. Depending on the type of nonlinearities, we show the existence of Turing patterns, the maxima of which may be of the spike or plateau type, and the existence of transition layer stationary solutions. These concepts are discussed on example of morphogenesis of the fresh water polyp Hydra, which is a model organism in developmental biology |
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