Turing conditions for pattern forming systems on evolving manifolds
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F21%3A00347490" target="_blank" >RIV/68407700:21340/21:00347490 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00285-021-01552-y" target="_blank" >https://doi.org/10.1007/s00285-021-01552-y</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00285-021-01552-y" target="_blank" >10.1007/s00285-021-01552-y</a>
Alternative languages
Result language
angličtina
Original language name
Turing conditions for pattern forming systems on evolving manifolds
Original language description
The study of pattern-forming instabilities in reaction-diffusion systems on growing or otherwise time-dependent domains arises in a variety of settings, including applications in developmental biology, spatial ecology, and experimental chemistry. Analyzing such instabilities is complicated, as there is a strong dependence of any spatially homogeneous base states on time, and the resulting structure of the linearized perturbations used to determine the onset of instability is inherently non-autonomous. We obtain general conditions for the onset and structure of diffusion driven instabilities in reaction-diffusion systems on domains which evolve in time, in terms of the time-evolution of the Laplace-Beltrami spectrum for the domain and functions which specify the domain evolution. Our results give sufficient conditions for diffusive instabilities phrased in terms of differential inequalities which are both versatile and straightforward to implement, despite the generality of the studied problem. These conditions generalize a large number of results known in the literature, such as the algebraic inequalities commonly used as a sufficient criterion for the Turing instability on static domains, and approximate asymptotic results valid for specific types of growth, or specific domains. We demonstrate our general Turing conditions on a variety of domains with different evolution laws, and in particular show how insight can be gained even when the domain changes rapidly in time, or when the homogeneous state is oscillatory, such as in the case of Turing-Hopf instabilities. Extensions to higher-order spatial systems are also included as a way of demonstrating the generality of the approach.
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
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Continuities
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
Journal of Mathematical Biology
ISSN
0303-6812
e-ISSN
1432-1416
Volume of the periodical
82
Issue of the periodical within the volume
1-2
Country of publishing house
DE - GERMANY
Number of pages
61
Pages from-to
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UT code for WoS article
000612909500004
EID of the result in the Scopus database
2-s2.0-85099904115