5 papers
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…