41 citations · 180 across the 23 of their papers we have counts for
7 papers · 1 filter
Stable and unstable spatially-periodic canards created in singular subcritical Turing bifurcations in the Brusselator system
Robert Jencks, Arjen Doelman, Tasso J. Kaper +1
In this article, we study the Brusselator partial differential equation (PDE) in the limit in which the diffusivity of the activator is much smaller than that of the inhibitor. The…
The evasion of tipping: pattern formation near a Turing-fold bifurcation
Dock Staal, Arjen Doelman
Model studies indicate that many climate subsystems, especially ecosystems, may be vulnerable to 'tipping': a 'catastrophic process' in which a system, driven by gradually changing…
Multi-front dynamics in spatially inhomogeneous Allen-Cahn equations
Robbin Bastiaansen, Arjen Doelman, Tasso J. Kaper
Recent studies of biological, chemical, and physical pattern-forming systems have started to go beyond the classic `near onset' and `far from equilibrium' theories for homogeneous…
Travelling pulses on three spatial scales in a Klausmeier-type vegetation-autotoxicity model
Paul Carter, Arjen Doelman, Annalisa Iuorio +1
Reaction-diffusion models describing interactions between vegetation and water reveal the emergence of several types of patterns and travelling wave solutions corresponding to stru…
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…
The existence of localized vegetation patterns in a systematically reduced model for dryland vegetation
Olfa Jaibi, Arjen Doelman, Martina Chirilus-Bruckner +1
In this paper we consider the 2-component reaction-diffusion model that was recently obtained by a systematic reduction of the 3-component Gilad et al. model for dryland ecosystem…