Results 51 to 60 of about 117,517 (263)
Turing Instability and Pattern Formation in an Activator-Inhibitor System with Nonlinear Diffusion
, 2014 In this work we study the effect of density dependent nonlinear diffusion on pattern formation in the Lengyel--Epstein system. Via the linear stability analysis we determine both the Turing and the Hopf instability boundaries and we show how nonlinear ...
Gambino, G. +2 more
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Spontaneous spatial fractal pattern formation in absorptive systems [PDF]
, 2012 We predict, for the first time to our knowledge, that purely-absorptive nonlinearity can support spontaneous spatial fractal pattern formation. A passive optical ring cavity with a thin slice of saturable absorber is analyzed.
Christian, J M +2 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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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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Most stable patterns among three-dimensional Turing patterns [PDF]
Japan Journal of Industrial and Applied Mathematics, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shoji, Hiroto, Yamada, Kohtaro
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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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Steady-state bifurcation of FHN-type oscillator on a square domain
Nonlinear Analysis, 2023 The Turing patterns of reaction-diffusion equations defined over a square region are more complex because of the D4-symmetry of the spatial region. This leads to the occurrence of multiple equivariant Turing bifurcations.
Chunrui Zhang +2 more
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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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Spatial pattern formation in chemical and biological systems [PDF]
, 1997 One of the central issues in developmental biology is the formation of spatial pattern in the embryo. A number of theories have been proposed to account for this phenomenon.
Chau, H. N. P. +2 more
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