Phase-space geometry of mass-conserving reaction-diffusion dynamics

F Brauns, J Halatek, E Frey - Physical Review X, 2020 - APS
Experimental studies of protein-pattern formation have stimulated new interest in the
dynamics of reaction-diffusion systems. However, a comprehensive theoretical …

Rethinking pattern formation in reaction–diffusion systems

J Halatek, E Frey - Nature Physics, 2018 - nature.com
The present theoretical framework for the analysis of pattern formation in complex systems is
mostly limited to the vicinity of fixed (global) equilibria. Here we present a new theoretical …

Nonideal Reaction-Diffusion Systems: Multiple Routes to Instability

T Aslyamov, F Avanzini, É Fodor, M Esposito - Physical Review Letters, 2023 - APS
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 …

Pattern localization to a domain edge

MC Wigbers, F Brauns, T Hermann, E Frey - Physical Review E, 2020 - APS
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 …

Strong defocusing of molecular reaction times results from an interplay of geometry and reaction control

DS Grebenkov, R Metzler, G Oshanin - Communications Chemistry, 2018 - nature.com
Textbook concepts of diffusion-versus kinetic-control are well-defined for reaction-kinetics
involving macroscopic concentrations of diffusive reactants that are adequately described by …

Pattern formation in reaction-diffusion systems with piecewise kinetic modulation: an example study of heterogeneous kinetics

M Kozák, EA Gaffney, V Klika - Physical Review E, 2019 - APS
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 …

Dynamical hierarchy in transition states: Why and how does a system climb over the mountain?

T Komatsuzaki, RS Berry - Proceedings of the National …, 2001 - National Acad Sciences
How a reacting system climbs through a transition state during the course of a reaction has
been an intriguing subject for decades. Here we present and quantify a technique to identify …

Heterogeneity induces spatiotemporal oscillations in reaction-diffusion systems

AL Krause, V Klika, TE Woolley, EA Gaffney - Physical Review E, 2018 - APS
We report on an instability arising in activator-inhibitor reaction-diffusion (RD) systems with a
simple spatial heterogeneity. This instability gives rise to periodic creation, translation, and …

Cross-diffusion-driven instability for reaction-diffusion systems: analysis and simulations

A Madzvamuse, HS Ndakwo, R Barreira - Journal of mathematical biology, 2015 - Springer
By introducing linear cross-diffusion for a two-component reaction-diffusion system with
activator-depleted reaction kinetics (Gierer and Meinhardt, Kybernetik 12: 30–39, 1972; …

Isolating patterns in open reaction–diffusion systems

AL Krause, V Klika, PK Maini, D Headon… - Bulletin of Mathematical …, 2021 - Springer
Realistic examples of reaction–diffusion phenomena governing spatial and spatiotemporal
pattern formation are rarely isolated systems, either chemically or thermodynamically …