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

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

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

Original language description

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.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

—

Continuities

S - Specificky vyzkum na vysokych skolach

Publication year

2017

Confidentiality

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

Name of the periodical

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

ISSN

1364-5021

e-ISSN

1471-2946

Volume of the periodical

473

Issue of the periodical within the volume

2199

Country of publishing house

GB - UNITED KINGDOM

Number of pages

19

Pages from-to

1-19

UT code for WoS article

000408469400012

EID of the result in the Scopus database

2-s2.0-85017592104