422 citations · 2.4k across the 156 of their papers we have counts for
9 papers · 2 filters
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…
Phase Oscillator Networks with Nonlocal Higher-Order Interactions: Twisted States, Stability and Bifurcations
Christian Bick, Tobias Böhle, Christian Kuehn
The Kuramoto model provides a prototypical framework to synchronization phenomena in interacting particle systems. Apart from full phase synchrony where all oscillators behave iden…
Computer Validation of Neural Network Dynamics: A First Case Study
Christian Kuehn, Elena Queirolo
A large number of current machine learning methods rely upon deep neural networks. Yet, viewing neural networks as nonlinear dynamical systems, it becomes quickly apparent that mat…
Mean field limits of co-evolutionary signed heterogeneous networks
Marios Antonios Gkogkas, Christian Kuehn, Chuang Xu
Many science phenomena are modelled as interacting particle systems (IPS) coupled on static networks. In reality, network connections are far more dynamic. Connections among indivi…
The hyperbolic umbilic singularity in fast-slow systems
Hildeberto Jardón-Kojakhmetov, Christian Kuehn, Maximilian Steinert
Fast-slow systems with three slow variables and gradient structure in the fast variables have, generically, hyperbolic umbilic, elliptic umbilic or swallowtail singularities. In th…
Discrete Geometric Singular Perturbation Theory
Samuel Jelbart, Christian Kuehn
We propose a mathematical formalism for discrete multi-scale dynamical systems induced by maps which parallels the established geometric singular perturbation theory for continuous…