4 papers · 1 filter
Graphons, Geometry, and Dynamics: Forward and Inverse Perspectives
Ágnes Backhausz, Christian Kuehn, Sjoerd van der Niet +1
In this work, we explore the interplay between graph limit theory, the geometry of underlying probability spaces, spectral theory, and network dynamical systems. We investigate two…
Emergent Higher-Order Structure from Fast Adaptive Networks
Christian Kuehn, Fergal Murphy
We study adaptive network models in which coupling weights evolve on a fast time scale relative to the phase dynamics of the nodes. Using Geometric Singular Perturbation Theory (GS…
Stability of Phase-Locked States in Signed Kuramoto Networks: Structure versus Adaptation
Jaeyoung Yoon, Christian Kuehn
Adaptive Kuramoto models admit a variety of nontrivial phase-locked configurations, including antipodal and rotating-wave states. A central open question is whether the observed pe…
Adaptive Cucker-Smale Networks: Limiting Laplacian Time-Varying Dynamics
Christian Kuehn, Jaeyoung Yoon
Differences in opinion can be seen as distances between individuals, and such differences do not always vanish over time. In this paper, we propose a modeling framework that captur…