Related papers: Turing instability for nonlocal heterogeneous reac…
The Turing instability is a paradigmatic route to patterns formation in reaction-diffusion systems. Following a diffusion-driven instability, homogeneous fixed points can become unstable when subject to external perturbation. As a…
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…
Biological, physical, medical, and numerical applications involving membrane problems on different scales are numerous. We propose an extension of the standard Turing theory to the case of two domains separated by a permeable membrane. To…
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 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…
In this paper we provide an example of a class of two reaction-diffusion-ODE equations with homogeneous Neumann boundary conditions, in which Turing-type instability not only destabilizes constant steady states but also induces blow-up of…
We analyze diffusion-driven (Turing) instability of a reaction-diffusion system. The innovation is that we replace the traditional Laplacian diffusion operator with a combination of the fourth order bi-Laplacian operator and the second…
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 developmental biology, spatial ecology, and experimental…
The problem of Turing instabilities for a reaction-diffusion system defined on a complex Cartesian product networks is considered. To this end we operate in the linear regime and expand the time dependent perturbation on a basis formed by…
Turing instabilities of reaction-diffusion systems can only arise if the diffusivities of the chemical species are sufficiently different. This threshold is unphysical in most systems with $N=2$ diffusing species, forcing experimental…
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…
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…
We hereby develop the theory of Turing instability for reaction-diffusion systems defined on complex networks assuming finite propagation. Extending to networked systems the framework introduced by Cattaneo in the 40's, we remove the…
The linearization principle states that the stability (or instability) of solutions to a suitable linearization of a nonlinear problem implies the stability (or instability) of solutions to the original nonlinear problem. In this work, we…
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…
This paper investigates pattern formation in reaction--diffusion systems with both diffusive and nondiffusive components, providing necessary and sufficient conditions for diffusion-driven instability (DDI) and establishing the existence of…
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 paper, I prove necessary and sufficient conditions for the existence of Turing instabilities in a general system with three interacting species. Turing instabilities describe situations when a stable steady state of a reaction…
Turing instability is a fundamental mechanism of nonequilibrium self-organization. However, despite the universality of its essential mechanism, Turing instability has thus far been investigated mostly in classical systems. In this study,…
Cooperative behaviors arising from bacterial cell-to-cell communication can be modeled by reaction-diffusion equations having only a single diffusible component. This paper presents the following three contributions for the systematic…