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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.14729 |
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| _version_ | 1866915689785196544 |
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| author | Guo, Yupeng Zaid, Ahmed A. A. Liu, Xueming Bianconi, Ginestra |
| author_facet | Guo, Yupeng Zaid, Ahmed A. A. Liu, Xueming Bianconi, Ginestra |
| contents | Collective synchronization in complex systems arises from the interplay between topology and dynamics, yet how to design and control such patterns in higher-order networks remains unclear. Here we show that a Dirac spectral programming framework enables programmable topological cluster synchronization on directed hypergraphs. By encoding tail-head hyperedges into a topological Dirac operator and introducing a tunable mass term, we obtain a spectrum whose isolated eigenvalues correspond to distinct synchronization clusters defined jointly on nodes and hyperedges. Selecting a target eigenvalue allows the system to self-organize toward the associated cluster state without modifying the underlying hypergraph structure. Simulations on directed-hypergraph block models and empirical systems--including higher-order contact networks and the ABIDE functional brain network--confirm that spectral selection alone determines the accessible synchronization patterns. Our results establish a general and interpretable route for controlling collective dynamics in directed higher-order systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14729 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topological cluster synchronization via Dirac spectral programming on directed hypergraphs Guo, Yupeng Zaid, Ahmed A. A. Liu, Xueming Bianconi, Ginestra Physics and Society Statistical Mechanics Mathematical Physics Adaptation and Self-Organizing Systems Data Analysis, Statistics and Probability Collective synchronization in complex systems arises from the interplay between topology and dynamics, yet how to design and control such patterns in higher-order networks remains unclear. Here we show that a Dirac spectral programming framework enables programmable topological cluster synchronization on directed hypergraphs. By encoding tail-head hyperedges into a topological Dirac operator and introducing a tunable mass term, we obtain a spectrum whose isolated eigenvalues correspond to distinct synchronization clusters defined jointly on nodes and hyperedges. Selecting a target eigenvalue allows the system to self-organize toward the associated cluster state without modifying the underlying hypergraph structure. Simulations on directed-hypergraph block models and empirical systems--including higher-order contact networks and the ABIDE functional brain network--confirm that spectral selection alone determines the accessible synchronization patterns. Our results establish a general and interpretable route for controlling collective dynamics in directed higher-order systems. |
| title | Topological cluster synchronization via Dirac spectral programming on directed hypergraphs |
| topic | Physics and Society Statistical Mechanics Mathematical Physics Adaptation and Self-Organizing Systems Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2512.14729 |