9 citations · 34 across the 8 of their papers we have counts for
8 papers
Degenerate Turing bifurcation and the birth of localised patterns in activator-inhibitor systems
Edgardo Villar-Sepúlveda, Alan R. Champneys
Precise conditions are provided for the existence and criticality of Turing bifurcations in a general class of activator-inhibitor reaction-diffusion equations on a one-dimensional…
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…
General conditions for Turing and wave instabilities in reaction-diffusion systems
Edgardo Villar-Sepúlveda, Alan R. Champneys
Necessary and sufficient conditions are provided for a diffusion-driven instability of a stable equilibrium of a reaction-diffusion system with components and a diagonal diffus…
Transient Instability and Patterns of Reactivity in Diffusive-Chemotaxis Soil Carbon Dynamics
Fasma Diele, Andrew L. Krause, Deborah Lacitignola +3
We study pattern formation in a chemotaxis model of bacteria and soil carbon dynamics as an example system where transient dynamics can give rise to pattern formation outside of Tu…
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…
Piecewise contracting maps on the interval: Hausdorff dimension, entropy and attractors
A. E. Calderón, E. Villar-Sepúlveda
We consider the attractor of a piecewise contracting map defined on a compact interval. If is injective, we show that it is possible to estimate the topological entropy…
A case study of multiple wave solutions in a reaction-diffusion system using invariant manifolds and global bifurcations
Edgardo Villar-Sepúlveda, Pablo Aguirre, Víctor F. Breña-Medina
A thorough analysis is performed to find traveling waves in a qualitative reaction-diffusion system inspired by a predator-prey model. We provide rigorous results coming from a sta…