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Turing Patterns and Biological Explanation [PDF]
Disputatio, 2017 AbstractTuring patterns are a class of minimal mathematical models that have been used to discover and conceptualize certain abstract features of early biological development. This paper examines a range of these minimal models in order to articulate and elaborate a philosophical analysis of their epistemic uses.
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Turing instabilities in general systems
, 2000 We present necessary and sufficient conditions on the stability matrix of a general n(S2)-dimensional reaction-diffusion system which guarantee that its uniform steady state can undergo a Turing bifurcation.
Satnoianu, RA +5 more
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Key Features of Turing Systems are Determined Purely by Network Topology
Physical Review X, 2018 Turing’s theory of pattern formation is a universal model for self-organization, applicable to many systems in physics, chemistry, and biology. Essential properties of a Turing system, such as the conditions for the existence of patterns and the ...
Xavier Diego +3 more
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Noise–Seeded Developmental Pattern Formation in Filamentous Cyanobacteria
Life, 2018 Under nitrogen-poor conditions, multicellular cyanobacteria such as Anabaena sp. PCC 7120 undergo a process of differentiation, forming nearly regular, developmental patterns of individual nitrogen-fixing cells, called heterocysts, interspersed between ...
Rinat Arbel-Goren +3 more
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Nonlinear Analysis, 2021 In this paper, we consider the dynamics of delayed Gierer–Meinhardt system, which is used as a classic example to explain the mechanism of pattern formation. The conditions for the occurrence of Turing, Hopf and Turing–Hopf bifurcation are established by
Shuangrui Zhao +2 more
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Turing Patterns in Deserts [PDF]
, 2012 Self-organised patterns of vegetation are a characteristic feature of many semi-arid regions. In particular, banded vegetation is typical on hillsides. Mathematical modelling is widely used to study these banded patterns, because there are no laboratory replicates.
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Unravelling the Turing bifurcation using spatially varying diffusion coefficients
, 1998 The Turing bifurcation is the basic bifurcation generating spatial pattern, and lies at the heart of almost all mathematical models for patterning in biology and chemistry.
Benson, Debbie L. +9 more
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Gene expression time delays & Turing pattern formation systems
, 2006 The incorporation of time delays can greatly affect the behaviour of partial differential equations and dynamical systems. In addition, there is evidence that time delays in gene expression due to transcription and translation play an important role in ...
Gaffney, Eamonn +5 more
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The effect of landscape fragmentation on Turing-pattern formation [PDF]
, 2022 Diffusion-driven instability and Turing pattern formation are a well-known mechanism by which the local interaction of species, combined with random spatial movement, can generate stable patterns of population densities in the absence of spatial ...
Lutscher, Frithjof +2 more
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Predator–prey pattern formation driven by population diffusion based on Moore neighborhood structure
Advances in Difference Equations, 2019 Diffusion-driven instability is a basic nonlinear mechanism for pattern formation. Therefore, the way of population diffusion may play a determinative role in the spatiotemporal dynamics of biological systems. In this research, we launch an investigation
Tousheng Huang +6 more
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