422 citations · 2.4k across the 156 of their papers we have counts for
16 papers · 1 filter
Bifurcations and Early-Warning Signs for SPDEs with Spatial Heterogeneity
Paolo Bernuzzi, Christian Kühn
Bistability is a key property of many systems arising in the nonlinear sciences. For example, it appears in many partial differential equations (PDEs). For scalar bistable reaction…
Reduction Methods in Climate Dynamics -- A Brief Review
Felix Hummel, Peter Ashwin, Christian Kuehn
We review a range of reduction methods that have been, or may be useful for connecting models of the Earth's climate system of differing complexity. We particularly focus on method…
Entry-exit functions in fast-slow systems with intersecting eigenvalues
Panagiotis Kaklamanos, Christian Kuehn, Nikola Popović +1
We study delayed loss of stability in a class of fast-slow systems with two fast variables and one slow one, where the linearisation of the fast vector field along a one-dimensiona…
Geometric Blow-Up for Folded Limit Cycle Manifolds in Three Time-Scale Systems
Samuel Jelbart, Christian Kuehn, Sara-Viola Kuntz
Geometric singular perturbation theory provides a powerful mathematical framework for the analysis of 'stationary' multiple time-scale systems which possess a critical manifold, i.…
Geometric blow-up of a dynamic Turing instability in the Swift-Hohenberg equation
Felix Hummel, Samuel Jelbart, Christian Kuehn
We present a rigorous analysis of the slow passage through a Turing bifurcation in the Swift-Hohenberg equation using a novel approach based on geometric blow-up. We show that the…
Geometric analysis of fast-slow PDEs with fold singularities via Galerkin discretisation
Maximilian Engel, Felix Hummel, Christian Kuehn +3
We study a singularly perturbed fast-slow system of two partial differential equations (PDEs) of reaction-diffusion type on a bounded domain via Galerkin discretisation. We assume…