Related papers: Instabilities and Patterns in Coupled Reaction-Dif…
In this paper we investigate the bifurcation structure of the triangular SKT model in the weak competition regime and of the corresponding fast-reaction system in 1D and 2D domains via numerical continuation methods. We show that the…
We consider a bulk-membrane-coupled partial differential equation in which a single diffusion equation posed within the unit ball is coupled to a two-component reaction diffusion equation posed on the bounding unit sphere through a linear…
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…
The linear stability of a shear layer in a highly diffusive stably stratified atmosphere has been investigated. This study completes and extends previous works by Dudis (1974) and Jones (1977). We show that: (i) an asymptotic regime is…
The problem of pattern formation in a generic two species reaction--diffusion model is studied, under the hypothesis that only one species can diffuse. For such a system, the classical Turing instability cannot take place. At variance, by…
Under certain conditions, focused laser excitation in semiconductor quantum well structures can lead to charge separation and a circular reaction front, which is visible as a ring-shaped photoluminescence pattern. The diffusion-reaction…
A general reaction-diffusion equation with spatiotemporal delay and homogeneous Dirichlet boundary condition is considered. The existence and stability of positive steady state solutions are proved via studying an equivalent…
A new class of patterns for multiplex networks is studied, which consists in a collection of different homogeneous states each referred to a distinct layer. The associated stability diagram exhibits a tricritical point, as a function of the…
Confirming Turing's theory of morphogens in developmental processes is challenging, and synthetic biology has opened new avenues for testing Turing's predictions. Synthetic mammalian pattern formation has been recently achieved through a…
Turing patterns emerge from a spatially uniform state following a linear instability driven by diffusion. Features of the eventual pattern (stabilized by non-linearities) are already present in the initial unstable modes. On a uniform flat…
Patterns of different symmetries may arise after solution to reaction-diffusion equations. Hexagonal arrays, layers and their perturbations are observed in different models after numerical solution to the corresponding initial-boundary…
A class of systems is considered, where immobile species associated to distinct patches, the nodes of a network, interact both locally and at a long-range, as specified by an (interaction) adjacency matrix. Non local interactions are…
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…
We study general linear transport-reaction systems on an arbitrary dimensional hypercube with periodic boundary conditions. Transport-reaction systems are often used to model the finite speed movement and interaction of particles, bacteria…
Mechanical properties of engineering alloys are strongly correlated to their microstructural length scale. Diffusive insta- bilities of the Mullins-Sekerka type is one of the principal mechanisms through which the scale of the…
In wall-bounded parallel flows, sustained turbulence can occur even while laminar flow is still stable. Channel flow is one of such flows and displays spatio-temporal fluctuating patterns of localized turbulence along its way from/to…
Our recent development of a novel research burner has made it possible to experimentally investigate truly unstretched and planar diffusion flames. Hence it has become feasible to directly validate theoretical models for thermal-diffusive…
Numerical simulations of a simple reaction--diffusion model reveal a surprising variety of irregular spatio--temporal patterns. These patterns arise in response to finite--amplitude perturbations. Some of them resemble the steady irregular…
In this paper we present computational techniques to investigate the solutions of two-component, nonlinear reaction-diffusion (RD) systems on arbitrary surfaces. We build on standard techniques for linear and nonlinear analysis of RD…
Effect of external periodic force on an oscillatory order in a reaction diffusion system (Gierer Meinhardt model) has been investigated. The 2:1 resonance situation is found susceptible for the generation of a band of phase instabilities.…