From one pattern into another: analysis of Turing patterns in heterogeneous domains via WKBJ

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F20%3A00338300" target="_blank" >RIV/68407700:21340/20:00338300 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1098/rsif.2019.0621" target="_blank" >https://doi.org/10.1098/rsif.2019.0621</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1098/rsif.2019.0621" target="_blank" >10.1098/rsif.2019.0621</a>

Result language

angličtina

Original language name

From one pattern into another: analysis of Turing patterns in heterogeneous domains via WKBJ

Original language description

Pattern formation from homogeneity is well studied, but less is known concerning symmetry-breaking instabilities in heterogeneous media. It is non-trivial to separate observed spatial patterning due to inherent spatial heterogeneity from emergent patterning due to nonlinear instability. We employ WKBJ asymptotics to investigate Turing instabilities for a spatially heterogeneous reaction-diffusion system, and derive conditions for instability which are local versions of the classical Turing conditions. We find that the structure of unstable modes differs substantially from the typical trigonometric functions seen in the spatially homogeneous setting. Modes of different growth rates are localized to different spatial regions. This localization helps explain common amplitude modulations observed in simulations of Turing systems in heterogeneous settings. We numerically demonstrate this theory, giving an illustrative example of the emergent instabilities and the striking complexity arising from spatially heterogeneous reaction-diffusion systems. Our results give insight both into systems driven by exogenous heterogeneity, as well as successive pattern forming processes, noting that most scenarios in biology do not involve symmetry breaking from homogeneity, but instead consist of sequential evolutions of heterogeneous states. The instability mechanism reported here precisely captures such evolution, and extends Turing's original thesis to a far wider and more realistic class of systems.

Czech name

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Czech description

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Type

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

CEP classification

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OECD FORD branch

10102 - Applied mathematics

Project

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Continuities

S - Specificky vyzkum na vysokych skolach

Publication year

2020

Confidentiality

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

Name of the periodical

JOURNAL OF THE ROYAL SOCIETY INTERFACE

ISSN

1742-5689

e-ISSN

1742-5662

Volume of the periodical

17

Issue of the periodical within the volume

162

Country of publishing house

GB - UNITED KINGDOM

Number of pages

15

Pages from-to

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UT code for WoS article

000507287900001

EID of the result in the Scopus database

2-s2.0-85077838286