6 papers
Vegetation pattern formation induced by local growth outpacing susceptibility to non-local competition
Jelle van der Voort, Ricardo Martinez-Garcia, Arjen Doelman
In this work, we present and analyze a general framework for vegetation dynamics in arid and semi-arid ecosystems in which non-local interactions are purely competitive. The genera…
Vegetation Patterning Can Both Impede and Trigger Critical Transitions from Savanna to Grassland
Jelle van der Voort, Mara Baudena, Ehud Meron +2
Tree-grass coexistence is a defining feature of savanna ecosystems, which play an important role in supporting biodiversity and human populations worldwide. While recent advances h…
The formation of periodic three-body orbits for Newtonian systems
Simon Portegies Zwart, Arjen Doelman, Jelmer Sein
Braids are periodic solutions to the general N-body problem in gravitational dynamics. These solutions seem special and unique, but they may result from rather usual encounters bet…
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…