422 citations · 2.4k across the 156 of their papers we have counts for
16 papers · 1 filter
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…
Rough center manifolds
Christian Kuehn, Alexandra Neamtu
Since the breakthrough in rough paths theory for stochastic ordinary differential equations (SDEs), there has been a strong interest in investigating the rough differential equatio…
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…
A gradient flow formulation for the stochastic Amari neural field model
Christian Kuehn, Jonas M. Tölle
We study stochastic Amari-type neural field equations, which are mean-field models for neural activity in the cortex. We prove that under certain assumptions on the coupling kernel…
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…