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Turing pattern with proportion preservation [PDF]
Journal of Theoretical Biology, 2006 Although Turing pattern is one of the most universal mechanisms for pattern formation, in its standard model the number of stripes changes with the system size, since the wavelength of the pattern is invariant: It fails to preserve the proportionality of the pattern, i.e., the ratio of the wavelength to the size, that is often required in biological ...
Ishihara, Shuji, Kaneko, Kunihiko
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Turing pattern outside of the Turing domain
Applied Mathematics Letters, 2007 There are two simple solutions to reaction-diffusion systems with limit-cycle reaction kinetics, producing oscillatory behaviour. The reaction parameter mu gives rise to a 'space-invariant' solution, and mu versus the ratio of the diffusion coefficients gives rise to a 'time-invariant' solution.
E. H. Flach +2 more
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Turing patterns in three dimensions [PDF]
Physical Review E, 2007 We investigate three-dimensional Turing patterns in two-component reaction diffusion systems. The FitzHugh-Nagumo equation, the Brusselator, and the Gray-Scott model are solved numerically in three dimensions. Several interconnected structures of domains as well as lamellar, hexagonal, and spherical domains are obtained as stable motionless equilibrium
Shoji, H, Yamada, K, Ueyama, D, Ohta, T
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Video1_Transient Turing patterns in a morphogenetic model.MP4
, 2022 One of the most surprising mechanisms to explain the symmetry breaking phenomenon linked to pattern formation is known as Turing instabilities. These patterns are self-organising spatial structures resulting from the interaction of at least two diffusive
Luis Diambra (200563) +1 more
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Spatiotemporal dynamics for a diffusive mussel–algae model near a Hopf bifurcation point
Advances in Difference Equations, 2021 In this paper, the Hopf bifurcation and Turing instability for a mussel–algae model are investigated. Through analysis of the corresponding kinetic system, the existence and stability conditions of the equilibrium and the type of Hopf bifurcation are ...
Shihong Zhong, Xuehan Cheng, Biao Liu
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Turing pattern design principles and their robustness [PDF]
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2021 Turing patterns have morphed from mathematical curiosities into highly desirable targets for synthetic biology. For a long time, their biological significance was sometimes disputed but there is now ample evidence for their involvement in processes ranging from skin pigmentation to digit and limb formation.
Sean T. Vittadello +3 more
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Video2_Transient Turing patterns in a morphogenetic model.MP4
, 2022 One of the most surprising mechanisms to explain the symmetry breaking phenomenon linked to pattern formation is known as Turing instabilities. These patterns are self-organising spatial structures resulting from the interaction of at least two diffusive
Luis Diambra (200563) +1 more
core +1 more source
Wavelength of a Turing-type mechanism regulates the morphogenesis of meshwork patterns
Scientific Reports, 2021 The meshwork pattern is a significant pattern in the development of biological tissues and organs. It is necessary to explore the mathematical mechanism of meshwork pattern formation.
Shan Guo, Ming-zhu Sun, Xin Zhao
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DataSheet1_Transient Turing patterns in a morphogenetic model.PDF
, 2022 One of the most surprising mechanisms to explain the symmetry breaking phenomenon linked to pattern formation is known as Turing instabilities. These patterns are self-organising spatial structures resulting from the interaction of at least two diffusive
Luis Diambra (200563) +1 more
core +1 more source
Discrete Dynamics in Nature and Society, 2020 The Turing pattern model is one of the theories used to describe organism formation patterns. Using this model, self-organized patterns emerge due to differences in the concentrations of activators and inhibitors. Here a cellular automata (CA)-like model
Takeshi Ishida
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