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Related papers: Non-Archimedean Models of Morphogenesis

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In this work, the influence of geometry and domain size on spatiotemporal pattern formation is investigated to establish parameter spaces for a cross-diffusive reaction-diffusion model on an annulus. By applying linear stability theory, we…

Dynamical Systems · Mathematics 2024-12-31 Gulsemay Yigit , Wakil Sarfaraz , Raquel Barreira , Anotida Madzvamuse

We give a comprehensive study of the analytic properties and long-time behavior of solutions of a reaction-diffusion system in a bounded domain in the case where the nonlinearity satisfies the standard monotonicity assumption. We pay the…

Analysis of PDEs · Mathematics 2020-06-11 Anna Kostianko , Chunyou Sun , Sergey Zelik

We study pattern formation in a chemotaxis model of bacteria and soil carbon dynamics as an example system where transient dynamics can give rise to pattern formation outside of Turing unstable regimes. We use a detailed analysis of the…

The formation of localized structures in the chlorine dioxide-idodine-malonic acid (CDIMA) reaction-diffusion system is investigated numerically using a realistic model of this system. We analyze the one-dimensional patterns formed along…

patt-sol · Physics 2009-10-31 S. Setayeshgar , M. C. Cross

Two front instabilities in a reaction-diffusion system are shown to lead to the formation of complex patterns. The first is an instability to transverse modulations that drives the formation of labyrinthine patterns. The second is a…

patt-sol · Physics 2009-10-28 Aric Hagberg , Ehud Meron

A new class of patterns for multiplex networks is studied, which consists in a collection of different homogeneous states each referred to a distinct layer. The associated stability diagram exhibits a tricritical point, as a function of the…

Statistical Mechanics · Physics 2018-01-26 Daniel M. Busiello , Timoteo Carletti , Duccio Fanelli

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…

Statistical Mechanics · Physics 2019-05-29 Joseph W. Baron , Tobias Galla

Understanding the pattern formation in communities has been at the center of attention in various fields. Here we introduce a novel model, called an "information-particle model," which is based on the reaction-diffusion model and the…

Physics and Society · Physics 2023-07-21 Junichi Miyakoshi

GTPase molecules are important regulators in cells that continuously run through an activation/deactivation and membrane-attachment/membrane-detachment cycle. Activated GTPase is able to localize in parts of the membranes and to induce cell…

Analysis of PDEs · Mathematics 2011-12-08 Andreas Rätz , Matthias Röger

Dynamical reaction-diffusion processes and meta-population models are standard modeling approaches for a wide variety of phenomena in which local quantities - such as density, potential and particles - diffuse and interact according to the…

Statistical Mechanics · Physics 2007-05-23 V. Colizza , R. Pastor-Satorras , A. Vespignani

In this article we formulate new models for coupled systems of bulk-surface reaction-diffusion equations on stationary volumes. The bulk reaction-diffusion equations are coupled to the surface reaction-diffusion equations through linear…

Analysis of PDEs · Mathematics 2015-06-23 Anotida Madzvamuse , Andy H. W. Chung , Chandrasekhar Venkataraman

A model of interacting random walkers is presented and shown to give rise to patterns consisting in periodic arrangements of fluctuating particle clusters. The model represents biological individuals that die or reproduce at rates depending…

Statistical Mechanics · Physics 2009-11-10 Cristobal Lopez , Emilio Hernandez-Garcia

We develop a general classification of the nature of the instabilities yielding spatial organization in open nonideal reaction-diffusion systems, based on linear stability analysis. This encompasses dynamics where chemical species diffuse,…

Statistical Mechanics · Physics 2023-10-05 Timur Aslyamov , Francesco Avanzini , Étienne Fodor , Massimiliano Esposito

We study diffusion-driven pattern-formation in networks of networks, a class of multilayer systems, where different layers have the same topology, but different internal dynamics. Agents are assumed to disperse within a layer by undergoing…

Physics and Society · Physics 2018-03-28 Andreas Brechtel , Philipp Gramlich , Daniel Ritterskamp , Barbara Drossel , Thilo Gross

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…

Pattern Formation and Solitons · Physics 2007-06-18 Hans G. Kaper , Shouhong Wang , Masoud Yari

The Turing instability paradigm is revisited in the context of a multispecies diffusion scheme derived from a self-consistent microscopic formulation. The analysis is developed with reference to the case of two species. These latter share…

Biological Physics · Physics 2012-07-02 Duccio Fanelli , Claudia Cianci , Francesca Di Patti

Self-organization, the ability of a system of microscopically interacting entities to shape macroscopically ordered structures, is ubiquitous in Nature. Spatio-temporal patterns are abundantly observed in a large plethora of applications,…

Pattern Formation and Solitons · Physics 2019-06-17 Malbor Asllani , Timoteo Carletti , Duccio Fanelli , Philip K. Maini

Turing patterns play a fundamental role in morphogenesis and population dynamics, encoding key information about the underlying biological mechanisms. Yet, traditional inverse problems have largely relied on non-biological data such as…

Analysis of PDEs · Mathematics 2025-09-10 Yuhan Li , Hongyu Liu , Catharine W. K. Lo

We study instabilities and pattern formation in reaction-diffusion layers that are diffusively coupled. For two-layer systems of identical two-component reactions, we analyze the stability of homogeneous steady states by exploiting the…

Pattern Formation and Solitons · Physics 2015-06-03 Anne J. Catlla , Amelia McNamara , Chad M. Topaz

Subcritical Turing bifurcations of reaction-diffusion systems in large domains lead to spontaneous onset of well-developed localised patterns via the homoclinic snaking mechanism. This phenomenon is shown to occur naturally when balancing…

Pattern Formation and Solitons · Physics 2025-06-10 Víctor Breña-Medina , Alan Champneys