Topological Dirac cluster synchronization on directed hypergraphs

[2512.14729] Topological Dirac cluster synchronization on directed hypergraphs Skip to main content Search Submit Donate Log in Physics > Physics and Society arXiv:2512.14729 (physics) [Submitted on 10 Dec 2025 ( v1 ), last revised 24 Aug 2026 (this version, v2)] Title: Topological Dirac cluster synchronization on directed hypergraphs Authors: Yupeng Guo , Ahmed A. A. Zaid , Xueming Liu , Ginestra Bianconi View PDF HTML (experimental) 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. Comments: (22 pages, 9 figures) Subjects: Physics and Society (physics.soc-ph) ; Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph); Adaptation and Self-Organizing Systems (nlin.AO); Data Analysis, Statistics and Probability (physics.data-an) Cite as: arXiv:2512.14729 [physics.soc-ph] (or arXiv:2512.14729v2 [physics.soc-ph] for this version) https://doi.org/10.48550/arXiv.2512.14729 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Ginestra Bianconi [ view email ] [v1] Wed, 10 Dec 2025 04:32:40 UTC (1,032 KB) [v2] Mon, 24 Aug 2026 21:40:48 UTC (3,578 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: physics.soc-ph < prev | next > new | recent | 2025-12 Change to browse by: cond-mat cond-mat.stat-mech math math-ph math.MP nlin nlin.AO physics physics.data-an References & Citations INSPIRE HEP SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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