422 citations · 2.4k across the 156 of their papers we have counts for
8 papers · 2 filters
On network dynamical systems with a nilpotent singularity
Hildeberto Jardón-Kojakhmetov, Christian Kuehn
Network dynamics is nowadays of extreme relevance to model and analyze complex systems. From a dynamical systems perspective, understanding the local behavior near equilibria is of…
Embedding Capabilities of Neural ODEs
Christian Kuehn, Sara-Viola Kuntz
A class of neural networks that gained particular interest in the last years are neural ordinary differential equations (neural ODEs). We study input-output relations of neural ODE…
Extending Discrete Geometric Singular Perturbation Theory to Non-Hyperbolic Points
Samuel Jelbart, Christian Kuehn
We extend the recently developed discrete geometric singular perturbation theory to the non-normally hyperbolic regime. Our primary tool is the Takens embedding theorem, which prov…
Persistent synchronization of heterogeneous networks with time-dependent linear diffusive coupling
Hildeberto Jardón-Kojakhmetov, Christian Kuehn, Iacopo P. Longo
We study synchronization for linearly coupled temporal networks of heterogeneous time-dependent nonlinear agents via the convergence of attracting trajectories of each node. The re…
Higher-Order Network Interactions through Phase Reduction for Oscillators with Phase-Dependent Amplitude
Christian Bick, Tobias Böhle, Christian Kuehn
Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction -- the reduction of the dynamics onto an invari…
Cross-diffusion induced instability on networks
Christian Kuehn, Cinzia Soresina
The concept of Turing instability, namely that diffusion can destabilize the uniform steady state, is well known either in the context of partial differential equations (PDEs) or i…
A Formal Geometric Blow-up Method for Pattern Forming Systems
Samuel Jelbart, Christian Kuehn
We extend and apply a recently developed approach to the study of dynamic bifurcations in PDEs based on the geometric blow-up method. We show that this approach, which has so far o…
Fast Reactions and Slow Manifolds
Christian Kuehn, Jan-Eric Sulzbach
In this paper we generalize the Fenichel theory for attracting critical/slow manifolds to fast-reaction systems in infinite dimensions. In particular, we generalize the theory of i…