5 papers
Graphons, Geometry, and Dynamics: Forward and Inverse Perspectives
Ágnes Backhausz, Christian Kuehn, Sjoerd van der Niet
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…
Symmetry-Breaking and Hysteresis in a Duplex Voter Model
Christian Kluge, Christian Kuehn
We introduce and analyze a voter-type model on a two-layer multiplex network, where the presence of a state on one layer acts as a catalyst or inhibitor to the propagation of that…
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…