Turing Instabilities are Not Enough to Ensure Pattern Formation

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F24%3A00372691" target="_blank" >RIV/68407700:21340/24:00372691 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1007/s11538-023-01250-4" target="_blank" >https://doi.org/10.1007/s11538-023-01250-4</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11538-023-01250-4" target="_blank" >10.1007/s11538-023-01250-4</a>

Result language

angličtina

Original language name

Turing Instabilities are Not Enough to Ensure Pattern Formation

Original language description

Symmetry-breaking instabilities play an important role in understanding the mechanisms underlying the diversity of patterns observed in nature, such as in Turing's reaction-diffusion theory, which connects cellular signalling and transport with the development of growth and form. Extensive literature focuses on the linear stability analysis of homogeneous equilibria in these systems, culminating in a set of conditions for transport-driven instabilities that are commonly presumed to initiate self-organisation. We demonstrate that a selection of simple, canonical transport models with only mild multistable non-linearities can satisfy the Turing instability conditions while also robustly exhibiting only transient patterns. Hence, a Turing-like instability is insufficient for the existence of a patterned state. While it is known that linear theory can fail to predict the formation of patterns, we demonstrate that such failures can appear robustly in systems with multiple stable homogeneous equilibria. Given that biological systems such as gene regulatory networks and spatially distributed ecosystems often exhibit a high degree of multistability and nonlinearity, this raises important questions of how to analyse prospective mechanisms for self-organisation.

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

2024

Confidentiality

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

Name of the periodical

BULLETIN OF MATHEMATICAL BIOLOGY

ISSN

0092-8240

e-ISSN

1522-9602

Volume of the periodical

86

Issue of the periodical within the volume

2

Country of publishing house

US - UNITED STATES

Number of pages

11

Pages from-to

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UT code for WoS article

001152210700002

EID of the result in the Scopus database

2-s2.0-85182823230