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Turing Bifurcations and Pattern Selection
1995Pattern forming instabilities in spatially extended dissipative systems driven away from equilibrium have been the focus of a large activity for many years. The goal of this chapter is to present some theoretical concepts that have been developed to understand and describe these dissipative structures [1] from a macroscopic point of view.
Borckmans, Pierre +3 more
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Turing patterns beyond hexagons and stripes
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2006The best known Turing patterns are composed of stripes or simple hexagonal arrangements of spots. Until recently, Turing patterns with other geometries have been observed only rarely. Here we present experimental studies and mathematical modeling of the formation and stability of hexagonal and square Turing superlattice patterns in a photosensitive ...
Lingfa, Yang +3 more
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Science, 2011
Turing patterns—self-organized structures created by systems that undergo reaction and diffusion—are a possible mechanism underlying pattern formation in living organisms. Although there are many experimental studies of two-dimensional (2D) pattern formation—three-dimensional (3D) structures, the most relevant to biology, have been difficult to observe
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Turing patterns—self-organized structures created by systems that undergo reaction and diffusion—are a possible mechanism underlying pattern formation in living organisms. Although there are many experimental studies of two-dimensional (2D) pattern formation—three-dimensional (3D) structures, the most relevant to biology, have been difficult to observe
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Turing pattern formation in heterogenous media
Physica D: Nonlinear Phenomena, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Voroney, J.-P. +2 more
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Galerkin model for Turing patterns on a sphere
Physical Review E, 2005We carry out a Lorenz-like truncation of reaction diffusion systems to investigate pattern formation on a spherical surface. Stability analysis suggests spots to be favored more than stripes in general. Numerical calculations on the truncated model are in agreement with the theoretical predictions.
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Turing Pattern Formation without Diffusion
2012Using the pigmentation pattern of zebrafish as the experimental system, we have been studying the mechanism of skin pattern formation. Recent findings of the cellular interactions among the two types of pigment cells, melanophores and xanthophores, are uncovering the cellular and molecular mechanisms.
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Localized Turing and Turing-Hopf Patterns
1995In systems driven away from thermodynamic equilibrium, patchiness often arises through the occurrence of symmetry breaking bifurcations. Diffusive instabilities resulting from differential diffusion processes acting in the presence of some autocatalytic kinetic scheme enter that class of phenomena to produce stationary space periodic (Turing) or ...
Borckmans, Pierre +5 more
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Turing-Turing bifurcation and multi-stable patterns in a Gierer-Meinhardt system
Applied Mathematical Modelling, 2022Hongbin Wang
exaly
Stochastic Turing patterns of trichomes in Arabidopsis leaves
Proceedings of the National Academy of Sciences of the United States of America, 2023Duccio Fanelli +2 more
exaly
Edge rewiring for network Turing patterns
Chaos: An Interdisciplinary Journal of Nonlinear ScienceExtending a framework originally proposed by Cencetti et al. [Eur. Phys. J. B 90, 1 (2017)], we investigate a topological control mechanism for mediating Turing patterns on unweighted, undirected networks. Our primary contribution is proving boundedness results involved in targeted destabilization, in which we map Laplacian mode shifts to structural ...
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