相关论文: Dynamical failure of Turing patterns
We derive a necessary and sufficient condition for Turing instabilities to occur in two-component systems of reaction-diffusion equations with Neumann boundary conditions. We apply this condition to reaction-diffusion systems built from…
Reaction diffusion systems are often used to study pattern formation in biological systems. However, most methods for understanding their behavior are challenging and can rarely be applied to complex systems common in biological…
The topological nature of the disorder of glasses and supercooled liquids strongly affects their high-frequency dynamics. In order to understand its main features, we analytically studied a simple topologically disordered model, where the…
A multi-phase-field model for the description of the discontinuous precipitation reaction is formulated which takes into account surface diffusion along grain boundaries and interfaces as well as volume diffusion. Simulations reveal that…
The propagation of unstable interfaces is at the origin of remarkable patterns that are observed in various areas of science as chemical reactions, phase transitions, growth of bacterial colonies. Since a scalar equation generates usually…
The possibility for the occurrence in crystals of a phenomenon, resembling turbulence, is discussed. This phenomenon, called {\it heterophase turbulence}, is manifested by the fluctuational appearance inside a crystalline sample of…
Time delays, modelling the process of intracellular gene expression, have been shown to have important impacts on the dynamics of pattern formation in reaction-diffusion systems. In particular, past work has shown that such time delays can…
The question of biological stability (permanence) of a replicator reaction-diffusion system is considered. Sufficient conditions of biological stability are found. It is proved that there are situations when biologically unstable…
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…
This article is concerned with the stability and long-time dynamics of structures arising from a structureless state. The paradigm is suggested by developmental biology, where morphogenesis is thought to result from a competition between…
Alan Turing's work in Morphogenesis has received wide attention during the past 60 years. The central idea behind his theory is that two chemically interacting diffusible substances are able to generate stable spatial patterns, provided…
We derive a simple sufficient condition for the local asymptotic stability of spatially discrete, continuous-time reaction-diffusion systems of networked dynamical systems at a homogeneous equilibrium point. The framework explicitly…
A driven system of three species of particle diffusing on a ring is studied in detail. The dynamics is local and conserves the three densities. A simple argument suggesting that the model should phase separate and break the translational…
Flow and Diffusion Distributed Structures (FDS) are stationary spatially periodic patterns that can be observed in reaction-diffusion-advection systems. These structures arise when the flow rate exceeds a certain bifurcation point provided…
We hereby develop the theory of Turing instability for reaction-diffusion systems defined on m-directed hypergraphs, the latter being generalization of hypergraphs where nodes forming hyperedges can be shared into two disjoint sets, the…
Localized patterns in singularly perturbed reaction-diffusion equations typically consist of slow parts -- in which the associated solution follows an orbit on a slow manifold in a reduced spatial dynamical system -- alternated by fast…
The universal equations describing collective oscillations of the multidomain patterns of small period in an arbitrary $d$-dimensional reaction-diffusion system of the activator-inhibitor type are asymptotically derived. It is shown that…
Dissipative structures are generally observed when a system relaxes from a far from equilibrium state. To address the reverse question given by the title, we investigate the relaxation process in a closed chemical reaction-diffusion system…
Patterns are ubiquitous in nature, but how they form is often unclear. Turing developed a seminal theory to explain patterns based on reactions that counteract the equalizing tendency of diffusion. These reactions require continuous energy…
An asymptotic method for finding instabilities of arbitrary $d$-dimensional large-amplitude patterns in a wide class of reaction-diffusion systems is presented. The complete stability analysis of 2- and 3-dimensional localized patterns is…