3 papers
math.AP2026
Compatibility of Higher-Order Slow-Manifold Reduction and Continuum Limits in Adaptive Networks
Christian Kuehn, Fergal Murphy, Jan-Eric Sulzbach
Adaptive networks couple the evolution of node states to the evolution of the interactions between them. In fast-adapting phase oscillator networks, a slow-manifold reduction of a…
math.DS2026
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…
math.CO2025
Simplicial Complex Emergence on Directed Hypergraphs
Christian Kuehn, Fergal Murphy
We study when co-evolving (or adaptive) higher-order networks defined on directed hypergraphs admit a simplicial description. Binary and triadic couplings are modelled by time-depe…