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math.DS2025
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…
math.DS2025
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…
math.DS2025
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…