相关论文: Simple and Superlattice Turing Patterns in Reactio…

Pattern formation mechanisms of a reaction-diffusion-advection system, with one diffusivity, differential advection, and (Robin) boundary conditions of Danckwerts type, are being studied. Pattern selection requires mapping the domains of…

Following the approach pioneered by Eckhaus, Mielke, Schneider, and others for reaction diffusion systems [E, M1, M2, S1, S2, SZJV], we systematically derive formally by multiscale expansion and justify rigorously by Lyapunov-Schmidt…

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…

Mechanisms of pattern formation---of which the Turing instability is an archetype---constitute an important class of dynamical processes occurring in biological, ecological and chemical systems. Recently, it has been shown that the Turing…

The Turing mechanism describes the emergence of spatial patterns due to spontaneous symmetry breaking in reaction-diffusion processes and underlies many developmental processes. Identifying Turing mechanisms in biological systems defines a…

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…

A recent Faraday wave experiment with two-frequency forcing reports two types of `superlattice' patterns that display periodic spatial structures having two separate scales [1]. These patterns both arise as secondary states once the primary…

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…

We investigate the influence of particle diffusion in the two-dimension contact process (CP) with a competitive dynamics in bipartite sublattices, proposed in [Phys. Rev. E 84, 011125 (2011)]. The particle creation depends on its first and…

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…

Turing patterns on unbounded domains have been widely studied in systems of reaction-diffusion equations. However, up to now, they have not been studied for systems of conservation laws. Here, we (i) derive conditions for Turing instability…

A cascade of phase transitions from square to hexagonal lattice is studied in 2D system of particles interacting via core-softened potential. Due to the presence of two length-scales of repulsion, different local configurations with four,…

Among living organisms, there are species that change their patterns on their body surface during their growth process and those that maintain their patterns. Theoretically, it has been shown that large-scale species do not form distinct…

This paper is concerned with analysis of coupled fractional reaction-diffusion equations. It provides analytical comparison for the fractional and regular reaction-diffusion systems. As an example, the reaction-diffusion model with cubic…

Turing patterns are stationary, wave-like structures that emerge from the nonequilibrium assembly of reactive and diffusive components. While they are foundational in biophysics, their classical formulation relies on a single characteristic…

We compare spot patterns generated by Turing mechanisms with those generated by replication cascades, in a model one-dimensional reaction-diffusion system. We determine the stability region of spot solutions in parameter space as a function…

We consider a class of singularly perturbed 2-component reaction-diffusion equations which admit bistable traveling front solutions, manifesting as sharp, slow-fast-slow, interfaces between stable homogeneous rest states. In many example…

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…

When two-dimensional pattern-forming problems are posed on a periodic domain, classical techniques (Lyapunov-Schmidt, equivariant bifurcation theory) give considerable information about what periodic patterns are formed in the transition…

We study physical properties of a Luttinger liquid in a superlattice which is characterized by alternating two tunneling parameters. Employing the Bosonization approach, we describe the corresponding Hubbard model by the equivalent…