Related papers: Generalized patterns from local and non local reac…
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…
We study a p-adic reaction-diffusion system and the associated Turing patterns. We establish an instability criteria and show that the Turing patterns are not classical patterns consisting of alternating domains. Instead of this, a Turing…
The modelling of linear and nonlinear reaction-subdiffusion processes is more subtle than normal diffusion and causes different phenomena. The resulting equations feature a spatial Laplacian with a temporal memory term through a time…
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…
Motivated by bacterial chemotaxis and multi-species ecological interactions in heterogeneous environments, we study a general one-dimensional reaction-cross-diffusion system in the presence of spatial heterogeneity in both transport and…
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…
A nonequilibrium system of locally interacting elements in a lattice with an absorbing order-disorder phase transition is studied under the effect of additional interacting fields. These fields are shown to produce interesting effects in…
Fully localised patterns involving cellular hexagons or squares have been found experimentally and numerically in various continuum models. However, there is currently no mathematical theory for the emergence of these localised cellular…
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…
Turing patterns formed by activator-inhibitor systems on networks are considered. The linear stability analysis shows that the Turing instability generally occurs when the inhibitor diffuses sufficiently faster than the activator. Numerical…
Long after Turing's seminal Reaction-Diffusion (RD) model, the elegance of his fundamental equations alleviated much of the skepticism surrounding pattern formation. Though Turing model is a simplification and an idealization, it is one of…
Experiments with networks of discrete reactive bistable electrochemical elements organized in regular and nonregular tree networks are presented to confirm an alternative to the Turing mechanism for the formation of self-organized…
The emergence of macroscopic order and patterns is a central paradigm in systems of (self-)propelled agents, and a key component in the structuring of many biological systems.The relationships between the ordering process and the underlying…
A feature common to many models of vegetation pattern formation in semi-arid ecosystems is a sequence of qualitatively different patterned states, "gaps -> labyrinth -> spots", that occurs as a parameter representing precipitation…
We develop a theory of the domain patterns in systems with competing short-range attractive interactions and long range repulsive Coulomb interactions. We take an energetic approach, in which patterns are considered as critical points of a…
Collective organisation of patterns into ring-like configurations has been well-studied when patterns are subject to either weak or semi-strong interactions. However, little is known numerically or analytically about their formation when…
Spatial pattern formation is a key feature of many natural systems in physics, chemistry and biology. The essential theoretical issue in understanding pattern formation is to explain how a spatially homogeneous initial state can undergo…
Spatial and temporal pattern formation in reaction-diffusion systems is typically studied with two or more equations, as scalar reaction-diffusion equations confined to convex domains do not admit stable inhomogeneous states in time or…
Reaction-diffusion systems have been proposed as a model for pattern formation and morphogenesis. The Fickian diffusion typically employed in these constructions model the Brownian motion of particles. The biological and chemical elements…
We derive a simple sufficient condition for the local asymptotic stability of spatially discrete, continuous-time reaction-diffusion systems of networked dynamical systems at a homogeneous equilibrium point. The framework explicitly…