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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

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10102 - Applied mathematics

Result continuities

  • Project

  • 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

  • UT code for WoS article

    000658179600001

  • EID of the result in the Scopus database

    2-s2.0-85107175056