9 citations · 19 across the 8 of their papers we have counts for
8 papers
Computation of Turing bifurcation normal form for n-component reaction-diffusion systems
Edgardo Villar-Sepúlveda, Alan R. Champneys
General expressions are derived for the amplitude equation valid at a Turing bifurcation of a system of reaction-diffusion equations in one spatial dimension, with an arbitrary num…
Amplitude equations for wave bifurcations in reaction-diffusion systems
Edgardo Villar-Sepúlveda, Alan R. Champneys
A wave bifurcation is the counterpart to a Turing instability in reaction-diffusion systems, but where the critical wavenumber corresponds to a pure imaginary pair rather than a ze…
Enhanced stability of pressure relief valves: mechanistic design and analysis
Hong Tang, Istvan Erdodi, Alan R. Champneys +1
Pressure-relief valves, often the critical last line of defence in process engineering, are known to be susceptible to valve chatter. Such behaviour has been shown to arise from a…
Bifurcation analysis of multiple limit cycles created in boundary equilibrium bifurcations in hybrid systems
Hong Tang, Alan Champneys, David Simpson
A boundary equilibrium bifurcation (BEB) in a hybrid dynamical system occurs when a regular equilibrium collides with a switching surface in phase space. This causes a transition t…
An Asymptotic Analysis of Spike Self-Replication and Spike Nucleation of Reaction-Diffusion Patterns on Growing 1-D Domains
Chunyi Gai, Edgardo Villar-Sepulveda, Alan Champneys +1
In the asymptotic limit of a large diffusivity ratio, certain two-component reaction-diffusion (RD) systems can admit localized spike solutions on a 1-D finite domain in a far-from…
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…
Designing reaction-cross-diffusion systems with Turing and wave instabilities
Edgardo Villar-Sepúlveda, Alan R. Champneys, Andrew L. Krause
General conditions are established under which reaction-cross-diffusion systems can undergo spatiotemporal pattern-forming instabilities. Recent work has focused on designing syste…
Pattern formation of bulk-surface reaction-diffusion systems in a ball
Edgardo Villar-Sepúlveda, Alan R. Champneys, Davide Cusseddu +1
Weakly nonlinear amplitude equations are derived for the onset of spatially extended patterns on a general class of n-component bulk-surface reaction-diffusion systems in a ball, u…