The study of pattern-forming instabilities in reaction–diffusion systems on growing or
otherwise time-dependent domains arises in a variety of settings, including applications in …

In this paper we establish a general theoretical framework for Turing diffusion-driven
instability for reaction-diffusion systems on time-dependent evolving domains. The main …

This paper deals with the study of spatial and spatio-temporal patterns in the reaction-
diffusion FitzHugh–Nagumo model on growing curved domains. This is carried out on two …

The theory of spatial pattern formation via Turing bifurcations–wherein an equilibrium of a
nonlinear system is asymptotically stable in the absence of dispersal but unstable in the …

A diffusively driven instability has been hypothesized as a mechanism to drive spatial self-
organization in biological systems since the seminal work of Turing. Such systems are often …

More than half a century ago Alan Turing showed that a system of nonlinear reaction-
diffusion equations could produce spatial patterns that are stationary and robust, a …

Reaction–diffusion systems are an intensively studied form of partial differential equation,
frequently used to produce spatially heterogeneous patterned states from homogeneous …

We study two-species reaction–diffusion systems on growing manifolds, including situations
where the growth is anisotropic yet dilational in nature. In contrast to the literature on linear …

Diffusion driven instability in reaction-diffusion systems has been proposed as a mechanism
for pattern formation in numerous embryological and ecological contexts. However, the …

By using asymptotic theory, we generalise the Turing diffusively-driven instability conditions
for reaction-diffusion systems with slow, isotropic domain growth. There are two fundamental …