Phase-space geometry of mass-conserving reaction-diffusion dynamics
Experimental studies of protein-pattern formation have stimulated new interest in the
dynamics of reaction-diffusion systems. However, a comprehensive theoretical …
dynamics of reaction-diffusion systems. However, a comprehensive theoretical …
Rethinking pattern formation in reaction–diffusion systems
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 …
mostly limited to the vicinity of fixed (global) equilibria. Here we present a new theoretical …
Nonideal Reaction-Diffusion Systems: Multiple Routes to Instability
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 …
organization in open nonideal reaction-diffusion systems, based on linear stability analysis …
Pattern localization to a domain edge
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 …
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
Textbook concepts of diffusion-versus kinetic-control are well-defined for reaction-kinetics
involving macroscopic concentrations of diffusive reactants that are adequately described by …
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 …
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 …
been an intriguing subject for decades. Here we present and quantify a technique to identify …
Heterogeneity induces spatiotemporal oscillations in reaction-diffusion systems
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 …
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; …
activator-depleted reaction kinetics (Gierer and Meinhardt, Kybernetik 12: 30–39, 1972; …
Isolating patterns in open reaction–diffusion systems
Realistic examples of reaction–diffusion phenomena governing spatial and spatiotemporal
pattern formation are rarely isolated systems, either chemically or thermodynamically …
pattern formation are rarely isolated systems, either chemically or thermodynamically …