Stable patterns with jump discontinuity in systems with Turing instability and hysteresis

Classical models of pattern formation are based on diffusion-driven instability (DDI) of constant stationary solutions of reaction-diffusion equations, which leads to emergence of stable, regular Turing patterns formed around that equilibrium. In this paper we show that coupling reaction-diffusion e...

Full description

Saved in:
Bibliographic Details
Main Authors: Härting, Steffen (Author) , Marciniak-Czochra, Anna (Author) , Takagi, Izumi (Author)
Format: Article (Journal) Chapter/Article
Language:English
Published: Feb 2016
In: Arxiv

Online Access:Verlag, kostenfrei, Volltext: http://arxiv.org/abs/1506.00881
Verlag, kostenfrei, Volltext: https://arxiv.org/pdf/1506.00881.pdf
Get full text
Author Notes:Steffen Härting, Anna Marciniak-Czochra, Izumi Takagi

MARC

LEADER 00000caa a2200000 c 4500
001 1561246166
003 DE-627
005 20220813203050.0
007 cr uuu---uuuuu
008 170727s2016 xx |||||o 00| ||eng c
035 |a (DE-627)1561246166 
035 |a (DE-576)491246161 
035 |a (DE-599)BSZ491246161 
035 |a (OCoLC)1340977874 
040 |a DE-627  |b ger  |c DE-627  |e rda 
041 |a eng 
084 |a 27  |2 sdnb 
100 1 |a Härting, Steffen  |e VerfasserIn  |0 (DE-588)1098456432  |0 (DE-627)857651366  |0 (DE-576)469142553  |4 aut 
245 1 0 |a Stable patterns with jump discontinuity in systems with Turing instability and hysteresis  |c Steffen Härting, Anna Marciniak-Czochra, Izumi Takagi 
264 1 |c Feb 2016 
300 |a 47 
336 |a Text  |b txt  |2 rdacontent 
337 |a Computermedien  |b c  |2 rdamedia 
338 |a Online-Ressource  |b cr  |2 rdacarrier 
500 |a Gesehen am 27.07.2017 
520 |a Classical models of pattern formation are based on diffusion-driven instability (DDI) of constant stationary solutions of reaction-diffusion equations, which leads to emergence of stable, regular Turing patterns formed around that equilibrium. In this paper we show that coupling reaction-diffusion equations with ordinary differential equations (ODE) may lead to a novel pattern formation phenomenon in which DDI causes destabilization of both constant solutions and Turing patterns. Bistability and hysteresis effects in the null sets of model nonlinearities yield formation of far from the equilibrium patterns with jump discontinuity. We derive conditions for stability of stationary solutions with jump discontinuity in a suitable topology which allows disclosing the discontinuity points and leads to the definition of ({\epsilon}0 , A)-stability. Additionally, we provide conditions on stability of patterns in a quasi-stationary model reduction. The analysis is illustrated on the example of three-component model of receptor-ligand binding. The proposed model provides an example of a mechanism of de novo formation of far from the equilibrium patterns in reaction-diffusion-ODE models involving co-existence of DDI and hysteresis. 
650 4 |a 35 
650 4 |a Mathematics - Analysis of PDEs 
700 1 |a Marciniak-Czochra, Anna  |d 1974-  |e VerfasserIn  |0 (DE-588)1044379626  |0 (DE-627)771928432  |0 (DE-576)397031505  |4 aut 
700 1 |a Takagi, Izumi  |e VerfasserIn  |0 (DE-588)1137271175  |0 (DE-627)894262696  |0 (DE-576)409770094  |4 aut 
773 0 8 |i Enthalten in  |t Arxiv  |d Ithaca, NY : Cornell University, 1991  |g (2016) Artikel-Nummer 1506.00881v2, 47 Seiten  |h Online-Ressource  |w (DE-627)509006531  |w (DE-600)2225896-6  |w (DE-576)28130436X  |7 nnas  |a Stable patterns with jump discontinuity in systems with Turing instability and hysteresis 
773 1 8 |g year:2016  |g extent:47  |a Stable patterns with jump discontinuity in systems with Turing instability and hysteresis 
856 4 0 |u http://arxiv.org/abs/1506.00881  |x Verlag  |z kostenfrei  |3 Volltext 
856 4 0 |u https://arxiv.org/pdf/1506.00881.pdf  |x Verlag  |z kostenfrei  |3 Volltext 
951 |a AR 
992 |a 20170727 
993 |a Article 
994 |a 2016 
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 2 
998 |g 1098456432  |a Härting, Steffen  |m 1098456432:Härting, Steffen  |d 110000  |d 110200  |d 110000  |d 110400  |e 110000PH1098456432  |e 110200PH1098456432  |e 110000PH1098456432  |e 110400PH1098456432  |k 0/110000/  |k 1/110000/110200/  |k 0/110000/  |k 1/110000/110400/  |p 1  |x j 
999 |a KXP-PPN1561246166  |e 2975267819 
BIB |a Y 
JSO |a {"physDesc":[{"extent":"47 S."}],"relHost":[{"title":[{"title":"Arxiv","title_sort":"Arxiv"}],"pubHistory":["1991 -"],"part":{"year":"2016","text":"(2016) Artikel-Nummer 1506.00881v2, 47 Seiten","extent":"47"},"titleAlt":[{"title":"Arxiv.org"},{"title":"Arxiv.org e-print archive"},{"title":"Arxiv e-print archive"},{"title":"De.arxiv.org"}],"type":{"media":"Online-Ressource","bibl":"edited-book"},"disp":"Stable patterns with jump discontinuity in systems with Turing instability and hysteresisArxiv","note":["Gesehen am 28.05.2024"],"language":["eng"],"recId":"509006531","origin":[{"dateIssuedKey":"1991","publisher":"Cornell University ; Arxiv.org","dateIssuedDisp":"1991-","publisherPlace":"Ithaca, NY ; [Erscheinungsort nicht ermittelbar]"}],"id":{"zdb":["2225896-6"],"eki":["509006531"]},"physDesc":[{"extent":"Online-Ressource"}]}],"origin":[{"dateIssuedKey":"2016","dateIssuedDisp":"Feb 2016"}],"id":{"eki":["1561246166"]},"name":{"displayForm":["Steffen Härting, Anna Marciniak-Czochra, Izumi Takagi"]},"type":{"bibl":"chapter","media":"Online-Ressource"},"note":["Gesehen am 27.07.2017"],"language":["eng"],"recId":"1561246166","title":[{"title":"Stable patterns with jump discontinuity in systems with Turing instability and hysteresis","title_sort":"Stable patterns with jump discontinuity in systems with Turing instability and hysteresis"}],"person":[{"display":"Härting, Steffen","roleDisplay":"VerfasserIn","role":"aut","family":"Härting","given":"Steffen"},{"roleDisplay":"VerfasserIn","display":"Marciniak-Czochra, Anna","role":"aut","family":"Marciniak-Czochra","given":"Anna"},{"display":"Takagi, Izumi","roleDisplay":"VerfasserIn","role":"aut","family":"Takagi","given":"Izumi"}]} 
SRT |a HAERTINGSTSTABLEPATT2016