History dependence and the continuum approximation breakdown: the impact of domain growth on Turing's instability

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F17%3A00313195" target="_blank" >RIV/68407700:21340/17:00313195 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1098/rspa.2016.0744" target="_blank" >http://dx.doi.org/10.1098/rspa.2016.0744</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1098/rspa.2016.0744" target="_blank" >10.1098/rspa.2016.0744</a>

Jazyk výsledku

angličtina

Název v původním jazyce

History dependence and the continuum approximation breakdown: the impact of domain growth on Turing's instability

Popis výsledku v původním jazyce

A diffusively driven instability has been hypothesized as a mechanism to drive spatial self-organization in biological systems since the seminal work of Turing. Such systems are often considered on a growing domain, but traditional theoretical studies have only treated the domain size as a bifurcation parameter, neglecting the system non-autonomy. More recently, the conditions for a diffusively driven instability on a growing domain have been determined under stringent conditions, including slow growth, a restriction on the temporal interval over which the prospect of an instability can be considered and a neglect of the impact that time evolution has on the stability properties of the homogeneous reference state from which heterogeneity emerges. Here, we firstly relax this latter assumption and observe that the conditions for the Turing instability are much more complex and depend on the history of the system in general. We proceed to relax all the above constraints, making analytical progress by focusing on specific examples. With faster growth, instabilities can grow transiently and decay, making the prediction of a prospective Turing instability much more difficult. In addition, arbitrarily high spatial frequencies can destabilize, in which case the continuum approximation is predicted to break down.

Název v anglickém jazyce

History dependence and the continuum approximation breakdown: the impact of domain growth on Turing's instability

Popis výsledku anglicky

A diffusively driven instability has been hypothesized as a mechanism to drive spatial self-organization in biological systems since the seminal work of Turing. Such systems are often considered on a growing domain, but traditional theoretical studies have only treated the domain size as a bifurcation parameter, neglecting the system non-autonomy. More recently, the conditions for a diffusively driven instability on a growing domain have been determined under stringent conditions, including slow growth, a restriction on the temporal interval over which the prospect of an instability can be considered and a neglect of the impact that time evolution has on the stability properties of the homogeneous reference state from which heterogeneity emerges. Here, we firstly relax this latter assumption and observe that the conditions for the Turing instability are much more complex and depend on the history of the system in general. We proceed to relax all the above constraints, making analytical progress by focusing on specific examples. With faster growth, instabilities can grow transiently and decay, making the prediction of a prospective Turing instability much more difficult. In addition, arbitrarily high spatial frequencies can destabilize, in which case the continuum approximation is predicted to break down.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

ISSN

1364-5021

e-ISSN

1471-2946

Svazek periodika

473

Číslo periodika v rámci svazku

2199

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

19

Strana od-do

1-19

Kód UT WoS článku

000408469400012

EID výsledku v databázi Scopus

2-s2.0-85017592104