Related papers: Imperfect Turing Patterns: Diffusiophoretic Assemb…
Self-organization in natural and engineered systems causes the emergence of ordered spatio-temporal motifs. In presence of diffusive species, Turing theory has been widely used to understand the formation of such patterns on continuous…
The Turing mechanism describes the emergence of spatial patterns due to spontaneous symmetry breaking in reaction-diffusion processes and underlies many developmental processes. Identifying Turing mechanisms in biological systems defines a…
This paper investigates the conditions for the stability and emergence of patterns in a new three-component reaction-diffusion system. The system describes the coexistence and interaction of water reservoirs, vegetation, and bushfire…
Since its introduction in 1952, Turing's (pre-)pattern theory ("the chemical basis of morphogenesis") has been widely applied to a number of areas in developmental biology. The related pattern formation models normally comprise a system of…
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,…
In this work we show that under specific anomalous diffusion conditions, chemical systems can produce well-ordered self-similar concentration patterns through a diffusion-driven instability. We also find spiral patterns and patterns with…
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…
Turing's reaction-diffusion theory of morphogenesis has been very successful in understanding macroscopic patterns within complex objects ranging from biological systems to sand dunes. However, this mechanism was never tested against…
We consider the classical Turing instability in a reaction-diffusion system as the secend part of our study on pattern formation. We prove that nonlinear dynamics of a general perturbation of the Turing instability is determined by the…
Turing patterns are a cornerstone of biological self-organization, yet their emergence typically requires finely tuned parameters occupying narrow regions of high-dimensional space. This poses a fundamental challenge: how can evolving…
Motivated by numerical simulations showing the emergence of either periodic or irregular patterns, we explore a mechanism of pattern formation arising in the processes described by a system of a single reaction-diffusion equation coupled…
The study of pattern emergence together with exploration of the exemplar Turing model is enjoying a renaissance both from theoretical and experimental perspective. Here, we implement a stability analysis of spatially dependent reaction…
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…
Disordered hyperuniform systems are exotic states of matter that completely suppress large-scale density fluctuations like crystals, and yet possess no Bragg peaks similar to liquids or glasses. Such systems have been discovered in a…
Spontaneous pattern formation in homogeneous systems is ubiquitous in nature. Although Turing demonstrated that spatial patterns can emerge in reaction-diffusion (RD) systems when the homogeneous state becomes linearly unstable, it remains…
Originating from the pioneering study of Alan Turing, the bifurcation analysis predicting spatial pattern formation from a spatially uniform state for diffusing morphogens or chemical species that interact through nonlinear reactions is a…
Intracellular protein patterns govern essential cellular functions by dynamically redistributing proteins between membrane-bound and cytosolic states, conserving their total numbers. This review presents a theoretical framework for…
Turing patterns in reaction-diffusion (RD) systems have classically been studied only in RD systems which do not explicitly depend on independent variables such as space. In practise, many systems for which Turing patterning is important…
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…
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…