Isolating Patterns in Open Reaction-Diffusion Systems
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F21%3A00350569" target="_blank" >RIV/68407700:21340/21:00350569 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s11538-021-00913-4" target="_blank" >https://doi.org/10.1007/s11538-021-00913-4</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11538-021-00913-4" target="_blank" >10.1007/s11538-021-00913-4</a>
Alternative languages
Result language
angličtina
Original language name
Isolating Patterns in Open Reaction-Diffusion Systems
Original language description
Realistic examples of reaction-diffusion phenomena governing spatial and spatiotemporal pattern formation are rarely isolated systems, either chemically or thermodynamically. However, even formulations of 'open' reaction-diffusion systems often neglect the role of domain boundaries. Most idealizations of closed reaction-diffusion systems employ no-flux boundary conditions, and often patterns will form up to, or along, these boundaries. Motivated by boundaries of patterning fields related to the emergence of spatial form in embryonic development, we propose a set of mixed boundary conditions for a two-species reaction-diffusion system which forms inhomogeneous solutions away from the boundary of the domain for a variety of different reaction kinetics, with a prescribed uniform state near the boundary. We show that these boundary conditions can be derived from a larger heterogeneous field, indicating that these conditions can arise naturally if cell signalling or other properties of the medium vary in space. We explain the basic mechanisms behind this pattern localization and demonstrate that it can capture a large range of localized patterning in one, two, and three dimensions and that this framework can be applied to systems involving more than two species. Furthermore, the boundary conditions proposed lead to more symmetrical patterns on the interior of the domain and plausibly capture more realistic boundaries in developmental systems. Finally, we show that these isolated patterns are more robust to fluctuations in initial conditions and that they allow intriguing possibilities of pattern selection via geometry, distinct from known selection mechanisms.
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
BULLETIN OF MATHEMATICAL BIOLOGY
ISSN
0092-8240
e-ISSN
1522-9602
Volume of the periodical
83
Issue of the periodical within the volume
7
Country of publishing house
US - UNITED STATES
Number of pages
35
Pages from-to
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UT code for WoS article
000658179600001
EID of the result in the Scopus database
2-s2.0-85107175056