422 citations · 2.4k across the 156 of their papers we have counts for
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The Role of Bifurcations in Parameter Estimation: A UQ Analysis of the Non-spatial Klausmeier Model
Lisa Beer, Christian Kuehn, Chiara Piazzola
We employ uncertainty quantification methods to investigate how parameter identifiability changes in the vicinity of a bifurcation point. We perform numerical experiments on the no…
Unstable Manifolds for the Kuramoto Model: Convergence to the Ott-Antonsen Manifold
Christian Kuehn, Giacomo Landi
In this paper, we study the finite-dimensional, homogeneous, all-to-all coupled Kuramoto model. We begin by performing a complete spectral analysis of all equilibria of the system.…
Normal Forms for Rough Differential Equations
Gideon Chiusole, Christian Kuehn, Maximilian Semenowicz
We address the existence of normal forms for rough ordinary differential equations. We assume suitable smoothness and the hyperbolicity of an equilibrium point. In this context, we…
Fréchet Means of Periodic Orbits in Dynamical Systems: Geometry, Dynamics, and Diagnostics
Paulina Hering, Christian Kuehn
In many dynamical systems applications, one seeks representative trajectories summarizing families of periodic orbits arising from parameter variation or uncertainty. While the Fré…
Synchronization for the Rough Kuramoto Model
Alexandra Blessing Neamtu, Christian Kuehn, Giacomo Landi +1
We study the local synchronization of phases and frequencies for the Kuramoto model driven by rough noise. In particular, we prove exponential convergence towards synchronization a…
A Dynamical Systems Perspective on the Analysis of Neural Networks
Dennis Chemnitz, Maximilian Engel, Christian Kuehn +1
In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide var…