Modern perspectives on near-equilibrium analysis of Turing systems
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F21%3A00352994" target="_blank" >RIV/68407700:21340/21:00352994 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1098/rsta.2020.0268" target="_blank" >https://doi.org/10.1098/rsta.2020.0268</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1098/rsta.2020.0268" target="_blank" >10.1098/rsta.2020.0268</a>
Alternative languages
Result language
angličtina
Original language name
Modern perspectives on near-equilibrium analysis of Turing systems
Original language description
In the nearly seven decades since the publication of Alan Turing's work on morphogenesis, enormous progress has been made in understanding both the mathematical and biological aspects of his proposed reaction-diffusion theory. Some of these developments were nascent in Turing's paper, and others have been due to new insights from modern mathematical techniques, advances in numerical simulations and extensive biological experiments. Despite such progress, there are still important gaps between theory and experiment, with many examples of biological patterning where the underlying mechanisms are still unclear. Here, we review modern developments in the mathematical theory pioneered by Turing, showing how his approach has been generalized to a range of settings beyond the classical two-species reaction-diffusion framework, including evolving and complex manifolds, systems heterogeneous in space and time, and more general reaction-transport equations. While substantial progress has been made in understanding these more complicated models, there are many remaining challenges that we highlight throughout. We focus on the mathematical theory, and in particular linear stability analysis of 'trivial' base states. We emphasize important open questions in developing this theory further, and discuss obstacles in using these techniques to understand biological reality. This article is part of the theme issue 'Recent progress and open frontiers in Turing's theory of morphogenesis'.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - 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
Result continuities
Project
<a href="/en/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Center for advanced applied science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
ISSN
1364-503X
e-ISSN
1471-2962
Volume of the periodical
379
Issue of the periodical within the volume
2213
Country of publishing house
GB - UNITED KINGDOM
Number of pages
30
Pages from-to
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UT code for WoS article
000715239400001
EID of the result in the Scopus database
2-s2.0-85118600508