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Fibration symmetries and cluster synchronization in multi-body systems
Margherita Bertè1, Tommaso Gili2
1IMT School for Advanced Studies, P.zza San Francesco 19, 55100, Lucca, Italy. margherita.berte@imtlucca.it.
Scientific Reports
|July 16, 2026
Summary
Structural symmetries in undirected hypergraphs influence complex system synchronization. Researchers identified node partitions based on incidence relations, revealing how these partitions relate to synchronization patterns in higher-order Kuramoto models.
Area of Science:
- Complex Systems
- Network Science
- Graph Theory
Background:
- Structural symmetries are crucial for synchronization in complex systems.
- Previous work established balanced partitions for synchrony in directed hypergraphs.
- Understanding synchronization in undirected hypergraphs requires new approaches.
Purpose of the Study:
- To identify node partitions in undirected hypergraphs based on incidence relations.
- To analyze the relationship between these partitions and synchronization behavior.
- To investigate the higher-order Kuramoto-Sakaguchi model on undirected hypergraphs.
Main Methods:
- Utilizing bipartite graph representations of undirected hypergraphs.
- Defining node partitions via equivalent incidence relations.
- Analyzing the higher-order Kuramoto-Sakaguchi model with specific conditions.
Main Results:
- Fibers were shown to define invariant synchrony subspaces for the Kuramoto-Sakaguchi model.
- The fibration partition was found to coincide with the synchrony partition under certain conditions.
- Algorithms and code were developed for computing local input equivalence and analyzing synchronization.
Conclusions:
- Node partitions based on incidence relations are key to understanding synchronization in undirected hypergraphs.
- The study provides tools and insights for analyzing and predicting synchronization in complex networks.
- Future work can explore topology adjustments for targeted synchronization patterns.
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