39 citations · 88 across the 7 of their papers we have counts for
8 papers
Large amplitude radially symmetric spots and gaps in a dryland ecosystem model
Eleanor Byrnes, Paul Carter, Arjen Doelman +1
We construct far-from-onset radially symmetric spot and gap solutions in a two-component dryland ecosystem model of vegetation pattern formation on flat terrain, using spatial dyna…
Criteria for the (in)stability of planar interfaces in singularly perturbed 2-component reaction-diffusion equations
Paul Carter, Arjen Doelman, Kaitlynn Lilly +2
We consider a class of singularly perturbed 2-component reaction-diffusion equations which admit bistable traveling front solutions, manifesting as sharp, slow-fast-slow, interface…
Localized radial roll patterns in higher space dimensions
Jason J. Bramburger, Dylan Altschuler, Chloe I. Avery +4
Localized roll patterns are structures that exhibit a spatially periodic profile in their center. When following such patterns in a system parameter in one space dimension, the len…
Enabling equation-free modeling via diffusion maps
Tracy Chin, Jacob Ruth, Clayton Sanford +3
Equation-free modeling aims at extracting low-dimensional macroscopic dynamics from complex high-dimensional systems that govern the evolution of microscopic states. This algorithm…
Pulse replication and accumulation of eigenvalues
Paul Carter, Jens D. M. Rademacher, Björn Sandstede
Motivated by pulse-replication phenomena observed in the FitzHugh--Nagumo equation, we investigate traveling pulses whose slow-fast profiles exhibit canard-like transitions. We sho…
Stable planar vegetation stripe patterns on sloped terrain in dryland ecosystems
Robbin Bastiaansen, Paul Carter, Arjen Doelman
In water-limited regions, competition for water resources results in the formation of vegetation patterns; on sloped terrain, one finds that the vegetation typically aligns in stri…