422 citations · 2.4k across the 156 of their papers we have counts for
12 papers · 2 filters
Multi-Population Phase Oscillator Networks with Higher-Order Interactions
Christian Bick, Tobias Böhle, Christian Kuehn
The classical Kuramoto model consists of finitely many pairwise coupled oscillators on the circle. In many applications a simple pairwise coupling is not sufficient to describe rea…
Reduced models of cardiomyocytes excitability: comparing Karma and FitzHugh-Nagumo
Maria Elena Gonzalez Herrero, Christian Kuehn, Krasimira Tsaneva-Atanasova
Since Noble adapted in 1962 the model of Hodgkin and Huxley to fit Purkinje fibres the refinement of models for cardiomyocytes has continued. Most of these models are high-dimensio…
A geometric analysis of the SIRS epidemiological model on a homogeneous network
Hildeberto Jardón-Kojakhmetov, Christian Kuehn, Andrea Pugliese +1
We study a fast-slow version of an SIRS epidemiological model on homogeneous graphs, obtained through the application of the moment closure method. We use GSPT to study the model,…
Estimating rate-induced tipping via asymptotic series and a Melnikov-like method
Christian Kuehn, Iacopo P. Longo
The paper deals with the study of rate-induced tipping in asymptotically autonomous scalar ordinary differential equations. We prove that, in such a tipping scenario, a solution wh…
Blowing-up Nonautonomous Vector Fields: Infinite Delay Equations and Invariant Manifolds
Luca Arcidiacono, Christian Kuehn
We show the existence of nonautonomous invariant manifolds for planar, asymptotically autonomous differential equations, that have equilibrium solutions with zero Lyapunov spectrum…
Slow Manifolds for Infinite-Dimensional Evolution Equations
Felix Hummel, Christian Kuehn
We extend classical finite-dimensional Fenichel theory in two directions to infinite dimensions. Under comparably weak assumptions we show that the solution of an infinite-dimensio…
Geometric analysis of a truncated Galerkin discretization of fast-slow PDEs with transcritical singularities
Maximilian Engel, Christian Kuehn
We consider a fast-slow partial differential equation (PDE) with reaction-diffusion dynamics in the fast variable and the slow variable driven by a differential operator on a bound…
Graphop Mean-Field Limits for Kuramoto-Type Models
Marios-Antonios Gkogkas, Christian Kuehn
Originally arising in the context of interacting particle systems in statistical physics, dynamical systems and differential equations on networks/graphs have permeated into a broa…
Metastable Speeds in the Fractional Allen-Cahn Equation
Franz Achleitner, Christian Kuehn, Jens Markus Melenk +1
We study numerically the one-dimensional Allen-Cahn equation with the spectral fractional Laplacian on intervals with homogeneous Neumann boundary conditions. In parti…
Coupled Dynamics on Hypergraphs: Master Stability of Steady States and Synchronization
Raffaella Mulas, Christian Kuehn, Jürgen Jost
In the study of dynamical systems on networks/graphs, a key theme is how the network topology influences stability for steady states or synchronized states. Ideally, one would like…
Homogenization of Fully-Coupled Chaotic Fast-Slow Systems via Intermediate Stochastic Regularization
Maximilian Engel, Marios-Antonios Gkogkas, Christian Kuehn
In this paper we study coupled fast-slow ordinary differential equations (ODEs) with small time scale separation parameter such that, for every fixed value of the slow variable…
A geometric analysis of the SIR, SIRS and SIRWS epidemiological models
Hildeberto Jardón-Kojakhmetov, Christian Kuehn, Andrea Pugliese +1
We study fast-slow versions of the SIR, SIRS, and SIRWS epidemiological models. The multiple time scale behavior is introduced to account for large differences between some of the…