Related papers: Extending the mathematical palette for development…

Many existing studies on pattern formation in the reaction-diffusion systems rely on deterministic models. However, environmental noise is often a major factor which leads to significant changes in the spatiotemporal dynamics. In this…

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…

Localised patterns are often observed in models for dryland vegetation, both as peaks of vegetation in a desert state and as gaps within a vegetated state, known as `fairy circles'. Recent results from radial spatial dynamics show that…

The problem of pattern formation in a generic two species reaction--diffusion model is studied, under the hypothesis that only one species can diffuse. For such a system, the classical Turing instability cannot take place. At variance, by…

Spatiotemporal patterns are common in biological systems. For electrically-coupled cells previous studies of pattern formation have mainly used external forcing as the main bifurcation parameter. The purpose of this paper is to show that…

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 systems. Recently, it has been shown that the Turing…

We study pattern formation in a chemotaxis model of bacteria and soil carbon dynamics as an example system where transient dynamics can give rise to pattern formation outside of Turing unstable regimes. We use a detailed analysis of the…

The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of…

We are surrounded by spatio-temporal patterns resulting from the interaction of the numerous basic units constituting natural or human-made systems. In presence of diffusive-like coupling, Turing theory has been largely applied to explain…

Diffusion models generate structure by progressively transforming noise into data, yet the mechanisms underlying this transition remain poorly understood. In this work, we show that pattern formation in trained diffusion models can be…

The rheological properties of biological tissues are core to processes such as cancer metastasis, wound healing and embryo development. The emergence of tissue and organ structures during morphogenesis requires the precise formation of…

Turing's mechanism is often invoked to explain periodic patterns in nature, although direct experimental support is scarce. Turing patterns form in reaction-diffusion systems when the activating species diffuse much slower than the…

We estimate density of defects frozen into a biological Turing pattern which was turned on at a finite rate. A self-locking of gene expression in individual cells, which makes the Turing transition discontinuous, stabilizes the pattern…

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…

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…

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…

Turing's theory of pattern formation has been used to describe the formation of self-organised periodic patterns in many biological, chemical and physical systems. However, the use of such models is hindered by our inability to predict, in…

MicroRNAs are extensively known for post-transcriptional gene regulation and pattern formation in the embryonic developmental stage. We explore the origin of these spatio-temporal patterns mathematically, considering three different motifs…

Elucidating the neurophysiological mechanisms underlying neural pattern formation remains an outstanding challenge in Computational Neuroscience. In this paper, we address the issue of understanding the emergence of neural patterns by…

Turing instabilities for a two species reaction-diffusion systems is studied under anisotropic diffusion. More specifically, the diffusion constants which characterize the ability of the species to relocate in space are direction sensitive.…