Related papers: Switch and template pattern formation in a discret…
The reaction-diffusion models have been extensively applied to explain the mechanism of pattern formations in early embryogenesis based on geometrically confined microtissues consisting of human pluripotent stem cells. Recently, mechanical…
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…
Originating from the pioneering study of Alan Turing, the bifurcation analysis predicting spatial pattern formation from a spatially uniform state for diffusing morphogens or chemical species that interact through nonlinear reactions is a…
MicroRNAs are extensively known for post-transcriptional gene regulation and pattern formation in the embryonic developmental stage. We explore the origin of these spatio-temporal patterns mathematically, considering three different motifs…
Many animals have patterned fur, feathers, or scales, such as the stripes of a zebra. Turing models, or reaction-diffusion systems, are a class of mathematical models of interacting species that have been successfully used to generate…
We explain the principles of gene expression pattern stabilization in systems of interacting, diffusible morphogens, with dynamically established source regions. Using a reaction-diffusion model with step-function production term, we…
We analyse a dynamic control problem for scalar reaction-diffusion equations, focusing on the emulation of pattern formation through the selection of appropriate active controls. While boundary controls alone prove inadequate for…
Many existing studies on pattern formation in the reaction-diffusion systems rely on deterministic models. However, environmental noise is often a major factor which leads to significant changes in the spatiotemporal dynamics. In this…
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…
We use various electrode layouts to tailor the profile of the electric field in a two-dimensional (2D) dielectric-barrier-discharge system, thereby creating spatial templates for the lateral distribution of discharge filaments. Our…
We consider a reaction-diffusion system including discontinuous hysteretic relay operators in reaction terms. This system is motivated by an epigenetic model that describes the evolution of a population of organisms which can switch their…
Spatiotemporal patterns are common in biological systems. For electrically-coupled cells previous studies of pattern formation have mainly used external forcing as the main bifurcation parameter. The purpose of this paper is to show that…
Precise temporal coordination of gene expression is crucial for many developmental processes. One central question in developmental biology is how such coordinated expression patterns are robustly controlled. During embryonic development of…
Motivated by recent experiments and models of biological segmentation, we analyze the exicitation of pattern-forming instabilities of convectively unstable reaction-diffusion-advection (RDA) systems, occuring by means of constant or…
Traveling fronts ubiquitous in physics, chemistry, and biology are prone to transverse cellular deformations due to diffusive or convective instabilities. Here we show both theoretically and experimentally that new patterns can be obtained…
The amoeboid organism, the plasmodium of Physarum polycephalum, behaves on the basis of spatio-temporal pattern formation by local contraction-oscillators. This biological system can be regarded as a reaction-diffusion system which has…
An important component in studying mathematical models in many biochemical systems, such as those found in developmental biology, is phase transition. The purpose of this work is to analyze the phase transition property of a…
We study pattern-forming instabilities in reaction-advection-diffusion systems. We develop an approach based on Lyapunov-Bloch exponents to figure out the impact of a spatially periodic mixing flow on the stability of a spatially…
Turing's mechanism is often invoked to explain periodic patterns in nature, although direct experimental support is scarce. Turing patterns form in reaction-diffusion systems when the activating species diffuse much slower than the…
Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion…