Related papers: A Selection Criterion for Patterns in Reaction-Dif…
We investigate dynamics near Turing patterns in reaction-diffusion systems posed on the real line. Linear analysis predicts diffusive decay of small perturbations. We construct a "normal form" coordinate system near such Turing patterns…
Reaction diffusion systems with Turing instability and mass conservation are studied. In such systems, abrupt decays of stripes follow quasi-stationary states in sequence. At steady state, the distance between stripes is much longer than…
The Turing patterning mechanism is believed to underly the formation of repetitive structures in development, such as zebrafish stripes and mammalian digits, but it has proved difficult to isolate the specific biochemical species…
Pattern formation is ubiquitous in nature and the mechanism widely-accepted to underlay them is based on the Turing instability, predicted by Alan Turing decades ago. This is a non-trivial mechanism that involves nonlinear interaction terms…
Patterns in reaction-diffusion systems often contain two spatial scales; a long scale determined by a typical wavelength or domain size, and a short scale pertaining to front structures separating different domains. Such patterns naturally…
Realistic examples of reaction-diffusion phenomena governing spatial and spatiotemporal pattern formation are rarely isolated systems, either chemically or thermodynamically. However, even formulations of `open' reaction-diffusion systems…
Several mechanisms have been proposed to explain the spontaneous generation of self-organized patterns, hypothesised to play a role in the formation of many of the magnificent patterns observed in Nature. In several cases of interest, the…
The diffusion-driven Turing instability is a potential mechanism for spatial pattern formation in numerous biological and chemical systems. However, engineering these patterns and demonstrating that they are produced by this mechanism is…
The formation of protein patterns inside cells is generically described by reaction-diffusion models. The study of such systems goes back to Turing, who showed how patterns can emerge from a homogenous steady state when two reactive…
This paper investigates the competition between both simple (e.g. stripes, hexagons) and ``superlattice'' (super squares, super hexagons) Turing patterns in two-component reaction-diffusion systems. ``Superlattice'' patterns are formed from…
This article is concerned with the stability and long-time dynamics of structures arising from a structureless state. The paradigm is suggested by developmental biology, where morphogenesis is thought to result from a competition between…
It is well known that simple reaction-diffusion systems can display very rich pattern formation behavior. Here we have studied two examples of such systems in three dimensions. First we investigate the morphology and stability of a generic…
This study investigates transient wave dynamics in Turing pattern formation, focusing on waves emerging from localised disturbances. While the traditional focus of diffusion-driven instability has primarily centred on stationary solutions,…
Among living organisms, there are species that change their patterns on their body surface during their growth process and those that maintain their patterns. Theoretically, it has been shown that large-scale species do not form distinct…
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…
Many animals have patterned fur, feathers, or scales, such as the stripes of a zebra. Turing models, or reaction-diffusion systems, are a class of mathematical models of interacting species that have been successfully used to generate…
Turing patterns play a fundamental role in morphogenesis and population dynamics, encoding key information about the underlying biological mechanisms. Yet, traditional inverse problems have largely relied on non-biological data such as…
Pattern formation from homogeneity is well-studied, but less is known concerning symmetry-breaking instabilities in heterogeneous media. It is nontrivial to separate observed spatial patterning due to inherent spatial heterogeneity from…
As proposed by Alan Turing in 1952 as a ubiquitous mechanism for nonequilibrium pattern formation, diffusional effects may destabilize uniform distributions of reacting chemical species and lead to both spatially and temporally…
Pattern formation is a visual understanding of the dynamics of complex systems. Patterns arise in many ways, such as the segmentation of animals, bacterial colonies during growth, vegetation, chemical reactions, etc. In most cases, the…