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    • Klika, Václav (3)
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All fields Title Creator / Publisher Keyword Year AND OR AND NOT All fields Title Creator / Publisher Keyword Year AND OR AND NOT All fields Title Creator / Publisher Keyword Year AND OR AND NOT All fields Title Creator / Publisher Keyword Year AND OR AND NOT All fields Title Creator / Publisher Keyword Year Sort by creator [A → Z]' creator [Z → A]' publishing year ↑ (asc)' publishing year ↓ (desc)' title [A → Z]' title [Z → A]' Simple Search Hits 1 – 3 of 3 1 Introduction to ‘Recent progress and open frontiers in Turing’s theory of morphogenesis’ Krause, Andrew L.; Gaffney, Eamonn A; Maini, Philip K.... In: Philos Trans A Math Phys Eng Sci (2021) BASE Show details 2 Modern perspectives on near-equilibrium analysis of Turing systems Krause, Andrew L.; Gaffney, Eamonn A.; Maini, Philip K.... In: Philos Trans A Math Phys Eng Sci (2021) BASE Show details 3 From one pattern into another: analysis of Turing patterns in heterogeneous domains via WKBJ Krause, Andrew L.; Klika, Václav; Woolley, Thomas E.; Gaffney, Eamonn A. In: J R Soc Interface (2020) Abstract: Pattern formation from homogeneity is well studied, but less is known concerning symmetry-breaking instabilities in heterogeneous media. It is non-trivial to separate observed spatial patterning due to inherent spatial heterogeneity from emergent patterning due to nonlinear instability. We employ WKBJ asymptotics to investigate Turing instabilities for a spatially heterogeneous reaction–diffusion system, and derive conditions for instability which are local versions of the classical Turing conditions. We find that the structure of unstable modes differs substantially from the typical trigonometric functions seen in the spatially homogeneous setting. Modes of different growth rates are localized to different spatial regions. This localization helps explain common amplitude modulations observed in simulations of Turing systems in heterogeneous settings. We numerically demonstrate this theory, giving an illustrative example of the emergent instabilities and the striking complexity arising from spatially heterogeneous reaction–diffusion systems. Our results give insight both into systems driven by exogenous heterogeneity, as well as successive pattern forming processes, noting that most scenarios in biology do not involve symmetry breaking from homogeneity, but instead consist of sequential evolutions of heterogeneous states. The instability mechanism reported here precisely captures such evolution, and extends Turing’s original thesis to a far wider and more realistic class of systems. Keyword: Life Sciences–Mathematics interface URL: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7014807/ https://doi.org/10.1098/rsif.2019.0621 http://www.ncbi.nlm.nih.gov/pubmed/31937231 BASE Hide details

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