Key features of Turing systems are determined purely by network topology
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 …
many systems in physics, chemistry, and biology. Essential properties of a Turing system …
Emergence of geometric turing patterns in complex networks
Turing patterns, arising from the interplay between competing species of diffusive particles,
have long been an important concept for describing nonequilibrium self-organization in …
have long been an important concept for describing nonequilibrium self-organization in …
Turing patterns in systems with high-order interactions
Turing theory of pattern formation is among the most popular theoretical means to account
for the variety of spatio-temporal structures observed in Nature and, for this reason, finds …
for the variety of spatio-temporal structures observed in Nature and, for this reason, finds …
Turing patterns mediated by network topology in homogeneous active systems
Mechanisms of pattern formation—of which the Turing instability is an archetype—constitute
an important class of dynamical processes occurring in biological, ecological, and chemical …
an important class of dynamical processes occurring in biological, ecological, and chemical …
Turing patterns in simplicial complexes
The spontaneous emergence of patterns in nature, such as stripes and spots, can be
mathematically explained by reaction-diffusion systems. These patterns are often referred as …
mathematically explained by reaction-diffusion systems. These patterns are often referred as …
Turing patterns in network-organized activator–inhibitor systems
H Nakao, AS Mikhailov - Nature Physics, 2010 - nature.com
Turing instability in activator–inhibitor systems provides a paradigm of non-equilibrium self-
organization; it has been extensively investigated for biological and chemical processes …
organization; it has been extensively investigated for biological and chemical processes …
Fluctuation-driven Turing patterns
T Butler, N Goldenfeld - Physical Review E—Statistical, Nonlinear, and Soft …, 2011 - APS
Models of diffusion-driven pattern formation that rely on the Turing mechanism are utilized in
many areas of science. However, many such models suffer from the defect of requiring fine …
many areas of science. However, many such models suffer from the defect of requiring fine …
[HTML][HTML] Pattern formation on networks: from localised activity to Turing patterns
N McCullen, T Wagenknecht - Scientific reports, 2016 - nature.com
Networks of interactions between competing species are used to model many complex
systems, such as in genetics, evolutionary biology or sociology and knowledge of the …
systems, such as in genetics, evolutionary biology or sociology and knowledge of the …
Stochastic Turing patterns in a synthetic bacterial population
D Karig, KM Martini, T Lu… - Proceedings of the …, 2018 - National Acad Sciences
The origin of biological morphology and form is one of the deepest problems in science,
underlying our understanding of development and the functioning of living systems. In 1952 …
underlying our understanding of development and the functioning of living systems. In 1952 …
Patterns of non-normality in networked systems
Several mechanisms have been proposed to explain the spontaneous generation of self-
organised patterns, hypothesised to play a role in the formation of many of the magnificent …
organised patterns, hypothesised to play a role in the formation of many of the magnificent …