Related papers: The Mean-Field Survival Model for Stripe Formation…

As zebrafish develop, black and gold stripes form across their skin due to the interactions of brightly colored pigment cells. These characteristic patterns emerge on the growing fish body, as well as on the anal and caudal fins. While…

The Turing patterning mechanism is believed to underly the formation of repetitive structures in development, such as zebrafish stripes and mammalian digits, but it has proved difficult to isolate the specific biochemical species…

Complex patterns emerge across a wide range of biological systems. While such patterns often exhibit remarkable robustness, variation and irregularity exist at multiple scales and can carry important information about the underlying agent…

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 numerically solve the active nematohydrodynamic equations of motion, coupled to a Turing reaction-diffusion model, to study the effect of active nematic flow on the stripe patterns resulting from a Turing instability. If the activity is…

In this paper we propose a "discrete in continuous" mathematical model for the morphogenesis of the posterior lateral line system in zebrafishes. Our model follows closely the results obtained in recent biological experiments. We rely on a…

Reaction diffusion systems with Turing instability and mass conservation are studied. In such systems, abrupt decays of stripes follow quasi-stationary states in sequence. At steady state, the distance between stripes is much longer than…

In this paper, we develop a mean-field model for simulating the microstructure evolution of crystalline materials during static recrystallization. The model considers a population of individual cells (i.e. grains and subgrains) growing in a…

It is common to use a compartmental, fluid model described by a system of ordinary differential equations (ODEs) to model disease spread. In addition to their simplicity, these models are also the mean-field approximations of more accurate…

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…

Turing instability in activator-inhibitor systems provides a paradigm of nonequilibrium pattern formation; it has been extensively investigated for biological and chemical processes. Turing pattern formation should furthermore be possible…

We study the mechanisms of pattern formation for vegetation dynamics in water-limited regions. Our analysis is based on a set of two partial differential equations (PDEs) of reaction-diffusion type for the biomass and water and one ordinary…

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…

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…

Complex contagion models that involve contagion along higher-order structures, such as simplicial complexes and hypergraphs, yield new classes of mean-field models. Interestingly, the differential equations arising from many such models…

Throughout developmental biology and ecology, transport can be driven by nonlocal interactions. Examples include cells that migrate based on contact with pseudopodia extended from other cells, and animals that move based on their vision of…

Collective behaviour in living systems is observed across many scales, from bacteria to insects, to fish shoals. Zebrafish have emerged as a model system amenable to laboratory study. Here we report a three-dimensional study 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…

Self-organized pattern behavior is ubiquitous throughout nature, from fish schooling to collective cell dynamics during organism development. Qualitatively these patterns display impressive consistency, yet variability inevitably exists…

Interactions between neighboring cells are essential for generating or refining patterns in a number of biological systems. We propose a discrete filtering approach to predict how networks of cells modulate spatially varying input signals…