Dresden 2026 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 8: Nonlinear Dynamics, Synchronization, and Chaos
DY 8.2: Vortrag
Montag, 9. März 2026, 09:45–10:00, ZEU/0118
Phase locking and multistability in the topological Kuramoto model on cell complexes — •Iva Bačić1,2, Michael T. Schaub3, Jürgen Kurths4, and Dirk Witthaut1,5 — 1Institute of Climate and Energy Systems: Energy Systems Engineering (ICE-1), Forschungszentrum Jülich, 52428 Jülich, Germany — 2Institute of Physics Belgrade, University of Belgrade, Serbia — 3RWTH Aachen University, Aachen, Germany — 4Potsdam Institute for Climate Impact Research (PIK), Potsdam, Germany — 5Institute for Theoretical Physics, University of Cologne, 50937 Köln, Germany
Higher-order group interactions fundamentally shape the dynamics and stability of oscillator networks. The topological Kuramoto model captures these effects by extending classical synchronization models to include interactions between cells of arbitrary dimension within simplicial and cell complexes. We present the topological nonlinear Kirchhoff conditions algorithm, a nonlinear generalization of Kirchhoff's circuit laws, that systematically identifies all phase-locked states in the topological Kuramoto model and reveals how higher-order topology governs multistability. Applying this framework to rings, Platonic solids, and simplexes, we uncover structural cascades of multistability inherited across dimensions, and demonstrate that cell complexes can exhibit richer multistability patterns than simplicial complexes of equal dimension. We find evidence hinting at universal multistability classes. Our results reveal how higher-order interactions affect synchronization and open new directions for understanding collective dynamics in systems with non-pairwise interactions.
Keywords: synchronization; higher-order interactions; Kuramoto model; multistability; simplicial and cell complexes