Communications Physics· 2026Q1
Topological Dirac cluster synchronization on directed hypergraphs
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- Q1SCImago
- 2026year
Short summary
A new dynamical systems framework allows designing specific synchronization patterns on directed hypergraphs by encoding hyperedges into a topological Dirac Hamiltonian, yielding isolated eigenstates that correspond to distinct synchronization clusters.
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Key points
- Proposes a dynamical systems framework for topological cluster synchronization on directed hypergraphs.
- Encodes oriented hyperedges into a topological Dirac Hamiltonian to generate a spectrum.
- Isolated eigenstates in the spectrum correspond to distinct synchronization cluster states on nodes and hyperedges.
- Allows designing synchronization patterns by selecting specific eigenstates without changing the hypergraph structure.
- Demonstrated on block models and empirical systems like contact networks and functional brain networks.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract Topological higher-order synchronization reveals collective phenomena demonstrating how topology shapes dynamics, yet providing a general theoretical framework for designing and controlling dynamical states on higher-order networks remains a challenge of the field. Here we propose a dynamical systems framework for topological cluster synchronization on directed hypergraphs that can be used to design synchronization patterns on nodes and hyperedges of directed hypergraphs. By encoding oriented hyperedges into the hypergraph topological Dirac Hamiltonian, we obtain a spectrum whose isolated eigenstates correspond to distinct topological synchronization cluster states defined jointly on nodes and hyperedges. By selecting any isolated eigenstate, the system can be driven toward the associated dynamical state reflecting a specific partition of the hypergraph without modifying the underlying hypergraph structure. We numerically demonstrate the ability to design different topological cluster synchronization states on directed-hypergraph block models and empirical systems-including higher-order contact networks and the ABIDE functional brain network. Our results establish a general and interpretable route for controlling collective dynamics in directed higher-order systems.
The authors' abstract, as published at the source. Communications Physics, 2026 · DOI ↗
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Field: Computer Networks and Communications
Computer Networks and CommunicationsComputer Science