Results 21 to 30 of about 5,421,281 (277)
Mathematics, 2023 This paper deals with the effects of partial differential equations on the development of spatiotemporal patterns in reaction–diffusion systems. These systems describe how the concentration of a certain substance is distributed in space or time under the
Ishtiaq Ali, Maliha Tehseen Saleem
semanticscholar +1 more source
Turing Patterning in Stratified Domains [PDF]
Bulletin of Mathematical Biology, 2020 AbstractReaction–diffusion processes across layered media arise in several scientific domains such as pattern-formingE. colion agar substrates, epidermal–mesenchymal coupling in development, and symmetry-breaking in cell polarization. We develop a modeling framework for bilayer reaction–diffusion systems and relate it to a range of existing models.
Andrew L. Krause +6 more
openaire +4 more sources
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
doaj +1 more source
Turing pattern prediction in three-dimensional domains: the role of initial conditions and growth
bioRxiv, 2023 Reaction-diffusion systems have been widely used to model pattern formation in biological systems. However, the emergence of Turing patterns in three-dimensional (3D) domains remains relatively unexplored.
S. Ben Tahar +3 more
semanticscholar +1 more source
Turing-Hopf patterns in a morphochemical model for electrodeposition with cross-diffusion
Applications in Engineering Science, 2021 This paper focuses on the impact of cross-diffusion for Turing-Hopf instability in a morphochemical model for electrodeposition (DIB) and completes the analysis on the role of cross-diffusion on pattern formation in electrodeposition we recently carried ...
Deborah Lacitignola +2 more
doaj +1 more source
A hybrid discrete-continuum approach to model Turing pattern formation. [PDF]
Mathematical biosciences and engineering : MBE, 2020 Since its introduction in 1952, with a further refinement in 1972 by Gierer and Meinhardt, Turing's (pre-)pattern theory (the chemical basis of morphogenesis) has been widely applied to a number of areas in developmental biology, where evolving cell and ...
Fiona R. Macfarlane +2 more
semanticscholar +1 more source
Turing Instabilities are Not Enough to Ensure Pattern Formation [PDF]
Bulletin of Mathematical Biology, 2023 Symmetry-breaking instabilities play an important role in understanding the mechanisms underlying the diversity of patterns observed in nature, such as in Turing’s reaction–diffusion theory, which connects cellular signalling and transport with the ...
Andrew L. Krause +4 more
semanticscholar +1 more source
Analytical detection of stationary Turing pattern in a predator-prey system with generalist predator
Mathematical Modelling of Natural Phenomena, 2022 A prey-predator model with prey dependent Holling type-II functional response and a generalist predator exhibits complex dynamics in response to parameter variation.
Subrata Dey, M. Banerjee, S. Ghorai
semanticscholar +1 more source
Fluctuation-driven Turing patterns [PDF]
Physical Review E, 2011 Minor changes to ...
Butler, Thomas, Goldenfeld, Nigel
openaire +3 more sources
Precision and dissipation of a stochastic Turing pattern. [PDF]
Physical Review E, 2020 Spontaneous pattern formation is a fundamental scientific problem that has received much attention since the seminal theoretical work of Turing on reaction-diffusion systems.
Shubhashis Rana, A. C. Barato
semanticscholar +1 more source