Related papers: Pattern formation in parabolic equations containin…
Bacteria can form a great variety of spatially heterogeneous cell density patterns, ranging from simple concentric rings to dynamical spiral waves appearing in growing colonies. These pattern formation phenomena are important as they…
Turing's theory of pattern formation has been used to describe the formation of self-organised periodic patterns in many biological, chemical and physical systems. However, the use of such models is hindered by our inability to predict, in…
Turing instabilities for a two species reaction-diffusion systems is studied under anisotropic diffusion. More specifically, the diffusion constants which characterize the ability of the species to relocate in space are direction sensitive.…
The diffusion equation is extended by including spatial-temporal memory in such a manner that the conservation of the concentration is maintained. The additional memory term gives rise to the formation of non-trivial stationary solutions.…
We have studied the entropy-driven mechanism leading to stationary patterns formation in stochastic systems with local dynamics and non-Fickian diffusion. We have shown that a multiplicative noise fulfilling a fluctuation-dissipation…
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…
The formation of protein patterns inside cells is generically described by reaction-diffusion models. The study of such systems goes back to Turing, who showed how patterns can emerge from a homogenous steady state when two reactive…
Hysteresis and bet-hedging (random choice of phenotypes) are two different observations typically linked with multiplicity of phenotypes in biological systems. Hysteresis can be viewed as form of the system's persistent memory of past…
Pattern formation is a visual understanding of the dynamics of complex systems. Patterns arise in many ways, such as the segmentation of animals, bacterial colonies during growth, vegetation, chemical reactions, etc. In most cases, the…
The paper treats a reaction-diffusion equation with hysteretic nonlinearity on a one-dimensional lattice. It arises as a result of the spatial discretization of the corresponding continuous model with so-called nontransverse initial data…
Cellular differentiation in a developping organism is studied via a discrete bistable reaction-diffusion model. A system of undifferentiated cells is allowed to receive an inductive signal emenating from its environment. Depending on the…
In this paper we are interested in a degenerate parabolic system of reaction-diffusion equations arising in biology when studying cell adhesion at the protein level. In this modeling the unknown is the couple of the distribution laws of the…
Several different enzymes display an apparent diffusion coefficient that increases with the concentration of their substrate. Moreover, their motion becomes directed in substrate gradients. Currently, there are several competing models for…
Many approaches to modelling reaction-diffusion systems with anomalous transport rely on deterministic equations and ignore fluctuations arising due to finite particle numbers. Starting from an individual-based model we use a…
In this paper we study a nonlinear reaction-diffusion system which models an infectious disease caused by bacteria such as those for cholera. One of the significant features in this model is that a certain portion of the recovered human…
In this paper we consider mathematical modeling of the dynamics of self-organized patterning of spatially confined human embryonic stem cells (hESCs) treated with BMP4 (gastruloids) described in recent experimental works. In the first part…
Materials undergoing both phase separation and chemical reactions (defined here as all processes that change particle type or number) form an important class of non-equilibrium systems. Examples range from suspensions of self-propelled…
For over 25 years it is known that the roll structure of electroconvection (EC) in the dielectric regime in planarly aligned nematic liquid crystals has, after a transition to defect chaos, the tendency to form chevron structures. We show,…
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…
Spatial and temporal pattern formation in reaction-diffusion systems is typically studied with two or more equations, as scalar reaction-diffusion equations confined to convex domains do not admit stable inhomogeneous states in time or…