131 citations · 534 across the 26 of their papers we have counts for
16 papers · 1 filter
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…
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…
Subcritical Turing bifurcation and the morphogenesis of localised patterns
Víctor Breña-Medina, Alan Champneys
Subcritical Turing bifurcations of reaction-diffusion systems in large domains lead to spontaneous onset of well-developed localised patterns via the homoclinic snaking mechanism.…
From Snaking to Isolas: A One-Active-Site Approximation in Discrete Optical Cavities
R. Kusdiantara, H. Susanto, A. R. Champneys
We investigate time-independent solutions of a discrete optical cavity model featuring saturable Kerr nonlinearity, a discrete version of the Lugiato-Lefever equation. This model s…
Organization of spatially localized structures near a codimension-three cusp-Turing bifurcation
P. Parra-Rivas, A. R. Champneys, F. Al-Sahadi +2
A wide variety of stationary or moving spatially localized structures is present in evolution problems on unbounded domains, governed by higher-than-second-order reversible spatial…
Dissecting the snake: the transition from localized patterns to isolated spikes in pattern formation systems
Nicolas Verschueren, Alan Champneys
An investigation is undertaken of coupled reaction-diffusion systems in one spatial dimension that are able to support, in different regions of their parameter space, either an iso…