422 citations · 2.4k across the 156 of their papers we have counts for
7 papers · 2 filters
Computing invariant sets of random differential equations using polynomial chaos
Maxime Breden, Christian Kuehn
Differential equations with random parameters have gained significant prominence in recent years due to their importance in mathematical modelling and data assimilation. In many ca…
Duck Traps: Two-dimensional Critical Manifolds in Planar Systems
Christian Kuehn, Christian Münch
In this work we consider two-dimensional critical manifolds in planar fast-slow systems near fold and so-called canard (=`duck') points. These higher-dimension, and lower-codimensi…
Power Network Dynamics on Graphons
Christian Kuehn, Sebastian Throm
Power grids are undergoing major changes from a few large producers to smart grids build upon renewable energies. Mathematical models for power grid dynamics have to be adapted to…
Discretized Fast-Slow Systems near Transcritical Singularities
Maximilian Engel, Christian Kuehn
We extend slow manifolds near a transcritical singularity in a fast-slow system given by the explicit Euler discretization of the corresponding continuous-time normal form. The ana…
Early-warning signals for bifurcations in random dynamical systems with bounded noise
Christian Kuehn, Giuseppe Malavolta, Martin Rasmussen
We consider discrete-time one-dimensional random dynamical systems with bounded noise, which generate an associated set-valued dynamical system. We provide necessary and sufficient…
Rigorous Validation of Stochastic Transition Paths
Maxime Breden, Christian Kuehn
Global dynamics in nonlinear stochastic systems is often difficult to analyze rigorously. Yet, many excellent numerical methods exist to approximate these systems. In this work, we…