Buchumschlag

Instability of turing patterns in reaction-diffusion-ODE systems

The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of interactions between cellular processes such as cell growth, di...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Marciniak-Czochra, Anna (VerfasserIn) , Karch, Grzegorz (VerfasserIn) , Suzuki, Kanako (VerfasserIn)
Dokumenttyp: Article (Journal)
Sprache:Englisch
Veröffentlicht: 2017
In: Journal of mathematical biology
Year: 2017, Jahrgang: 74, Heft: 3, Pages: 583-618
ISSN:1432-1416
DOI:10.1007/s00285-016-1035-z
Online-Zugang:Verlag, Volltext: http://dx.doi.org/10.1007/s00285-016-1035-z
Verlag, Volltext: https://link.springer.com/article/10.1007/s00285-016-1035-z
Verlag, Volltext: https://link.springer.com/content/pdf/10.1007%2Fs00285-016-1035-z.pdf
Volltext
Verfasserangaben:Anna Marciniak-Czochra, Grzegorz Karch, Kanako Suzuki

MARC

LEADER 00000caa a2200000 c 4500
001 1561208892
003 DE-627
005 20220813202910.0
007 cr uuu---uuuuu
008 170726s2017 xx |||||o 00| ||eng c
024 7 |a 10.1007/s00285-016-1035-z  |2 doi 
035 |a (DE-627)1561208892 
035 |a (DE-576)491208898 
035 |a (DE-599)BSZ491208898 
035 |a (OCoLC)1340977873 
040 |a DE-627  |b ger  |c DE-627  |e rda 
041 |a eng 
084 |a 32  |2 sdnb 
100 1 |a Marciniak-Czochra, Anna  |d 1974-  |e VerfasserIn  |0 (DE-588)1044379626  |0 (DE-627)771928432  |0 (DE-576)397031505  |4 aut 
245 1 0 |a Instability of turing patterns in reaction-diffusion-ODE systems  |c Anna Marciniak-Czochra, Grzegorz Karch, Kanako Suzuki 
264 1 |c 2017 
300 |a 36 
336 |a Text  |b txt  |2 rdacontent 
337 |a Computermedien  |b c  |2 rdamedia 
338 |a Online-Ressource  |b cr  |2 rdacarrier 
500 |a First online 15 June 2016 
500 |a Gesehen am 26.07.2017 
520 |a The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of interactions between cellular processes such as cell growth, differentiation or transformation and diffusing signaling factors. We focus on stability analysis of solutions of a prototype model consisting of a single reaction-diffusion equation coupled to an ordinary differential equation. We show that such systems are very different from classical reaction-diffusion models. They exhibit diffusion-driven instability (turing instability) under a condition of autocatalysis of non-diffusing component. However, the same mechanism which destabilizes constant solutions of such models, destabilizes also all continuous spatially heterogeneous stationary solutions, and consequently, there exist no stable Turing patterns in such reaction-diffusion-ODE systems. We provide a rigorous result on the nonlinear instability, which involves the analysis of a continuous spectrum of a linear operator induced by the lack of diffusion in the destabilizing equation. These results are extended to discontinuous patterns for a class of nonlinearities. 
700 1 |a Karch, Grzegorz  |e VerfasserIn  |0 (DE-588)1119925223  |0 (DE-627)873033469  |0 (DE-576)409787655  |4 aut 
700 1 |a Suzuki, Kanako  |e VerfasserIn  |0 (DE-588)1119925789  |0 (DE-627)873637720  |0 (DE-576)409787663  |4 aut 
773 0 8 |i Enthalten in  |t Journal of mathematical biology  |d Berlin : Springer, 1974  |g 74(2017), 3, Seite 583-618  |h Online-Ressource  |w (DE-627)242065082  |w (DE-600)1421292-4  |w (DE-576)065026489  |x 1432-1416  |7 nnas  |a Instability of turing patterns in reaction-diffusion-ODE systems 
773 1 8 |g volume:74  |g year:2017  |g number:3  |g pages:583-618  |g extent:36  |a Instability of turing patterns in reaction-diffusion-ODE systems 
856 4 0 |u http://dx.doi.org/10.1007/s00285-016-1035-z  |x Verlag  |x Resolving-System  |3 Volltext 
856 4 0 |u https://link.springer.com/article/10.1007/s00285-016-1035-z  |x Verlag  |3 Volltext 
856 4 0 |u https://link.springer.com/content/pdf/10.1007%2Fs00285-016-1035-z.pdf  |x Verlag  |3 Volltext 
951 |a AR 
992 |a 20170726 
993 |a Article 
994 |a 2017 
998 |g 1044379626  |a Marciniak-Czochra, Anna  |m 1044379626:Marciniak-Czochra, Anna  |d 110000  |d 110200  |d 110000  |d 110400  |e 110000PM1044379626  |e 110200PM1044379626  |e 110000PM1044379626  |e 110400PM1044379626  |k 0/110000/  |k 1/110000/110200/  |k 0/110000/  |k 1/110000/110400/  |p 1  |x j 
999 |a KXP-PPN1561208892  |e 2975195834 
BIB |a Y 
SER |a journal 
JSO |a {"language":["eng"],"recId":"1561208892","type":{"bibl":"article-journal","media":"Online-Ressource"},"note":["First online 15 June 2016","Gesehen am 26.07.2017"],"person":[{"family":"Marciniak-Czochra","given":"Anna","roleDisplay":"VerfasserIn","display":"Marciniak-Czochra, Anna","role":"aut"},{"given":"Grzegorz","family":"Karch","role":"aut","display":"Karch, Grzegorz","roleDisplay":"VerfasserIn"},{"display":"Suzuki, Kanako","roleDisplay":"VerfasserIn","role":"aut","family":"Suzuki","given":"Kanako"}],"title":[{"title_sort":"Instability of turing patterns in reaction-diffusion-ODE systems","title":"Instability of turing patterns in reaction-diffusion-ODE systems"}],"relHost":[{"physDesc":[{"extent":"Online-Ressource"}],"origin":[{"publisherPlace":"Berlin ; Heidelberg ; New York","dateIssuedKey":"1974","publisher":"Springer","dateIssuedDisp":"1974-"}],"id":{"issn":["1432-1416"],"zdb":["1421292-4"],"eki":["242065082"]},"disp":"Instability of turing patterns in reaction-diffusion-ODE systemsJournal of mathematical biology","note":["Gesehen am 17.10.05"],"type":{"media":"Online-Ressource","bibl":"periodical"},"language":["eng"],"recId":"242065082","pubHistory":["1.1974/75 -"],"titleAlt":[{"title":"Mathematical biology"}],"part":{"issue":"3","pages":"583-618","year":"2017","extent":"36","text":"74(2017), 3, Seite 583-618","volume":"74"},"title":[{"title":"Journal of mathematical biology","title_sort":"Journal of mathematical biology"}]}],"physDesc":[{"extent":"36 S."}],"name":{"displayForm":["Anna Marciniak-Czochra, Grzegorz Karch, Kanako Suzuki"]},"id":{"doi":["10.1007/s00285-016-1035-z"],"eki":["1561208892"]},"origin":[{"dateIssuedKey":"2017","dateIssuedDisp":"2017"}]} 
SRT |a MARCINIAKCINSTABILIT2017 

Ähnliche Einträge