English
Related papers

Related papers: Classification of parameter spaces for reaction-di…

200 papers

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

This work explores the influence of domain size of a non-compact two dimensional annular domain on the evolution of pattern formation that is modelled by an \textit{activator-depleted} reaction-diffusion system. A closed form expression is…

Dynamical Systems · Mathematics 2018-07-06 Wakil Sarfaraz , Anotida Madzvamuse

In this work an activator-depleted reaction-diffusion system is investigated on polar coordinates with the aim of exploring the relationship and the corresponding influence of domain size on the types of possible diffusion-driven…

Dynamical Systems · Mathematics 2018-01-11 Wakil Sarfaraz , Anotida Madzvamuse

The study of pattern-forming instabilities in reaction-diffusion systems on growing or otherwise time-dependent domains arises in a variety of settings, including applications in developmental biology, spatial ecology, and experimental…

Pattern Formation and Solitons · Physics 2022-07-11 Robert A. Van Gorder , Václav Klika , Andrew L. Krause

The aim of this work is to study the effect of diffusion on the stability of the equilibria in a general two-components reaction-diffusion system with Neumann boundary conditions in the space of continuous functions. As by product, we…

Analysis of PDEs · Mathematics 2023-12-19 Francisco J. Vielma-Leal , Miguel A. D. R. Palma , Miguel Montenegro-Concha

Pattern formation mechanisms of a reaction-diffusion-advection system, with one diffusivity, differential advection, and (Robin) boundary conditions of Danckwerts type, are being studied. Pattern selection requires mapping the domains of…

Pattern Formation and Solitons · Physics 2009-11-23 Arik Yochelis , Moshe Sheintuch

We analyzed conditions for Hopf and Turing instabilities to occur in two-component fractional reaction-diffusion systems. We showed that the eigenvalue spectrum and fractional derivative order mainly determine the type of instability and…

Adaptation and Self-Organizing Systems · Physics 2009-12-09 B. Y. Datsko , V. V. Gafiychuk

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…

Mathematical Physics · Physics 2007-05-23 Rui Dilao

We investigate Turing instability and pattern formation in two-dimensional domains for two reaction-diffusion models, obtained as diffusive limits of kinetic equations for mixtures of monatomic and polyatomic gases. The first model is of…

Mathematical Physics · Physics 2026-02-23 Stefano Boccelli , Giorgio Martalò , Romina Travaglini

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…

Pattern Formation and Solitons · Physics 2019-11-06 Michal Kozák , Eamonn A Gaffney , Václav Klika

The reaction-diffusion processes in a growing domain involves a dilution term that modifies the properties of the homogeneous state that, in contrast to a fixed domain, depends on time. We study how the dilution term changes the steady…

Pattern Formation and Solitons · Physics 2023-08-24 Aldo Ledesma-Durán

We analyze diffusion-driven (Turing) instability of a reaction-diffusion system. The innovation is that we replace the traditional Laplacian diffusion operator with a combination of the fourth order bi-Laplacian operator and the second…

Spectral Theory · Mathematics 2018-07-04 Jooyeon Chung

On a two-dimensional circular domain, we analyze the formation of spatio-temporal patterns for a class of coupled bulk-surface reaction-diffusion models for which a passive diffusion process occurring in the interior bulk domain is linearly…

Pattern Formation and Solitons · Physics 2020-08-11 Frédéric Paquin-Lefebvre , Wayne Nagata , Michael J. Ward

Motivated by bacterial chemotaxis and multi-species ecological interactions in heterogeneous environments, we study a general one-dimensional reaction-cross-diffusion system in the presence of spatial heterogeneity in both transport and…

Pattern Formation and Solitons · Physics 2023-03-08 Eamonn A. Gaffney , Andrew L. Krause , Philip K. Maini , Chenyuan Wang

Hyperbolic reaction-diffusion equations have recently attracted attention both for their application to a variety of biological and chemical phenomena, and for their distinct features in terms of propagation speed and novel instabilities…

Pattern Formation and Solitons · Physics 2022-08-17 Joshua Ritchie , Andrew L. Krause , Robert A. Van Gorder

Reaction-diffusion processes across layered media arise in several scientific domains such as pattern-forming E. coli on agar substrates, epidermal-mesenchymal coupling in development, and symmetry-breaking in cell polarisation. We develop…

Pattern Formation and Solitons · Physics 2020-09-18 Andrew L. Krause , Václav Klika , Jacob Halatek , Paul K. Grant , Thomas E. Woolley , Neil Dalchau , Eamonn A. Gaffney

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

For delayed reaction-diffusion Schnakenberg systems with Neumann boundary conditions, critical conditions for Turing instability are derived, which are necessary and sufficient. And existence conditions for Turing, Hopf and Turing-Hopf…

Dynamical Systems · Mathematics 2020-01-08 Weihua Jiang , Hongbin Wang , Xun Cao

In the past the study of reaction-diffusion systems has greatly contributed to our understanding of the behavior of many-body systems far from equilibrium. In this paper we aim at characterizing the properties of diffusion limited reactions…

Statistical Mechanics · Physics 2015-05-14 Sven Dorosz , Michel Pleimling

Patterns in reaction-diffusion systems often contain two spatial scales; a long scale determined by a typical wavelength or domain size, and a short scale pertaining to front structures separating different domains. Such patterns naturally…

patt-sol · Physics 2009-10-22 Aric Hagberg , Ehud Meron
‹ Prev 1 2 3 10 Next ›