33 citations · 152 across the 23 of their papers we have counts for
11 papers · 1 filter
Integral Asymptotics, Coalescing Saddles, and Multiple-scales Analysis of a Generalised Swift-Hohenberg Equation
Václav Klika, Mohit P. Dalwadi, Andrew L. Krause +1
Integral asymptotics play an important role in the analysis of differential equations and in a variety of other settings. In this work, we apply an integral asymptotics approach to…
Pattern Localisation in the Swift-Hohenberg Equation via Slowly Varying Spatial Heterogeneity
Andrew L. Krause, Václav Klika, Edgardo Villar-Sepúlveda +2
Theories of localised pattern formation are important to understand a broad range of natural patterns, but are less well-understood than more established mechanisms of domain-filli…
On the speed of propagation in Turing patterns for reaction-diffusion systems
Václav Klika, Eamonn A. Gaffney, Philip K. Maini
This study investigates transient wave dynamics in Turing pattern formation, focusing on waves emerging from localised disturbances. While the traditional focus of diffusion-driven…
Turing instabilities are not enough to ensure pattern formation
Andrew L. Krause, Eamonn A. Gaffney, Thomas Jun Jewell +2
Symmetry-breaking instabilities play an important role in understanding the mechanisms underlying the diversity of patterns observed in nature, such as in Turing's reaction--diffus…
Modern Perspectives on Near-Equilibrium Analysis of Turing Systems
Andrew L. Krause, Eamonn A. Gaffney, Philip K. Maini +1
In the nearly seven decades since the publication of Alan Turing's work on morphogenesis, enormous progress has been made in understanding both the mathematical and biological aspe…
WKBJ approximation for linearly coupled systems: asymptotics of reaction-diffusion systems
Juraj Kováč, Václav Klika
Asymptotic analysis has become a common approach in investigations of reaction-diffusion equations and pattern formation, especially when considering generalizations to the origina…
Isolating Patterns in Open Reaction-Diffusion Systems
Andrew L. Krause, Václav Klika, Philip K. Maini +2
Realistic examples of reaction-diffusion phenomena governing spatial and spatiotemporal pattern formation are rarely isolated systems, either chemically or thermodynamically. Howev…
Turing Patterning in Stratified Domains
Andrew L. Krause, Václav Klika, Jacob Halatek +4
Reaction-diffusion processes across layered media arise in several scientific domains such as pattern-forming E. coli on agar substrates, epidermal-mesenchymal coupling in developm…
Pattern formation in reaction-diffusion systems with piece-wise kinetic modulation: an example study of heterogeneous kinetics
Michal Kozák, Eamonn A Gaffney, Václav Klika
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 impleme…
From One Pattern into Another: Analysis of Turing Patterns in Heterogeneous Domains via WKBJ
Andrew L. Krause, Václav Klika, Thomas E. Woolley +1
Pattern formation from homogeneity is well-studied, but less is known concerning symmetry-breaking instabilities in heterogeneous media. It is nontrivial to separate observed spati…
Turing conditions for pattern forming systems on evolving manifolds
Robert A. Van Gorder, Václav Klika, Andrew L. Krause
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 d…