Related papers: Effect of randomness and anisotropy on Turing patt…
It is well known that simple reaction-diffusion systems can display very rich pattern formation behavior. Here we have studied two examples of such systems in three dimensions. First we investigate the morphology and stability of a generic…
Hyperbolic reaction-diffusion equations have recently attracted attention both for their application to a variety of biological and chemical phenomena, and for their distinct features in terms of propagation speed and novel instabilities…
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…
Reaction-diffusion processes on networked systems have received mounting attention in the past two decades, and the corresponding theory of network dynamics has been continuously enriched with the advancement of network science. Recently,…
We explore a mechanism of pattern formation arising in processes described by a system of a single reaction-diffusion equation coupled with ordinary differential equations. Such systems of equations arise from the modeling of interactions…
We numerically study the anisotropic Turing patterns (TPs) of an activator-inhibitor system, focusing on anisotropic diffusion by using the Finsler geometry (FG) modeling technique. In the FG modeling prescription, the diffusion…
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…
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…
Classical models of pattern formation are based on diffusion-driven instability (DDI) of constant stationary solutions of reaction-diffusion equations, which leads to emergence of stable, regular Turing patterns formed around that…
In this paper, the Turing instability in reaction-diffusion models defined on complex networks is studied. Here, we focus on three types of models which generate complex networks, i.e. the Erd\H{o}s-R\'enyi, the Watts-Strogatz, and the…
The process of pattern formation for a multi-species model anchored on a time varying network is studied. A non homogeneous perturbation superposed to an homogeneous stable fixed point can amplify, as follows a novel mechanism of…
Pattern formation in reaction-diffusion systems where the diffusion terms correspond to a Sturm-Liouville problem are studied. These correspond to a problem where the diffusion coefficient depends on the spatial variable: $\nabla \cdot…
A number of evidences suggests that thick-film resistors are close to a metal-insulator transition and that tunneling processes between metallic grains are the main source of resistance. We consider as a minimal model for description of…
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…
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…
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…
It is well known that for reaction-diffusion systems with differential isotropic diffusions, a Turing instability yields striped solutions. In this paper we study the impact of weak anisotropy by directional advection on such solutions, and…
This paper proposes an agent-based model which reproduces different structures of animal groups. The shape and structure of the group is the effect of simple interaction rules among individuals: each animal deploys itself depending on the…
By discretising space into compartments and letting system dynamics be governed by the reaction-diffusion master equation, it is possible to derive and simulate a stochastic model of reaction and diffusion on an arbitrary domain. However,…
We performed an extensive numerical study of a two-dimensional reaction-diffusion system of the activator-inhibitor type in which domain patterns can form. We showed that both multidomain and labyrinthine patterns may form spontaneously as…