{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T23:32:20Z","timestamp":1772494340911,"version":"3.50.1"},"reference-count":53,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T00:00:00Z","timestamp":1768953600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12375031"],"award-info":[{"award-number":["12375031"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11875135"],"award-info":[{"award-number":["11875135"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In the study of disordered hyperuniformity, which bridges ordered and disordered states and has broad implications in physics and biology, active matter systems offer a rich platform for spontaneous pattern formation. This work investigates frustrated Vicsek\u2013Kuramoto systems, where frustration induces complex collective behaviors, to explore how hyperuniform states arise. We numerically analyze the phase diagram via the structure factor\u00a0S(q)\u00a0and the density variance\u00a0\u27e8\u03b4\u03c12R\u27e9. Results show that recessive lattice states exhibit Class I hyperuniformity under high coupling strength and intermediate frustration, emerging from the interplay of frustration-induced periodicity and active motion, characterized by dynamic, drifting rotation centers rather than static order. Notably, global hyperuniformity emerges from the spatial complementarity of orientation subgroups that are individually non-hyperuniform, a phenomenon termed \u201corientation-modulated hyperuniformity\u201d. This work establishes frustration as a novel mechanism for generating hyperuniform states in active matter, highlighting how anisotropic interactions can yield global order from disordered components, with potential relevance to biological systems and material science.<\/jats:p>","DOI":"10.3390\/e28010126","type":"journal-article","created":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T13:59:54Z","timestamp":1769003994000},"page":"126","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Orientation-Modulated Hyperuniformity in Frustrated Vicsek\u2013Kuramoto Systems"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-4877-8244","authenticated-orcid":false,"given":"Yichen","family":"Lu","sequence":"first","affiliation":[{"name":"Institute of Systems Science, Huaqiao University, Xiamen 361021, China"},{"name":"School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-2127-4951","authenticated-orcid":false,"given":"Tong","family":"Zhu","sequence":"additional","affiliation":[{"name":"Institute of Systems Science, Huaqiao University, Xiamen 361021, China"},{"name":"College of Information Science and Technology, Huaqiao University, Xiamen 361021, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-1161-5359","authenticated-orcid":false,"given":"Yingshan","family":"Guo","sequence":"additional","affiliation":[{"name":"Institute of Systems Science, Huaqiao University, Xiamen 361021, China"},{"name":"College of Mechanical Engineering and Automation Science and Technology, Huaqiao University, Xiamen 361021, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9558-6021","authenticated-orcid":false,"given":"Yunyun","family":"Li","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1421-0442","authenticated-orcid":false,"given":"Zhigang","family":"Zheng","sequence":"additional","affiliation":[{"name":"Institute of Systems Science, Huaqiao University, Xiamen 361021, China"},{"name":"College of Information Science and Technology, Huaqiao University, Xiamen 361021, China"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"041113","DOI":"10.1103\/PhysRevE.68.041113","article-title":"Local density fluctuations, hyperuniformity, and order metrics","volume":"68","author":"Torquato","year":"2003","journal-title":"Phys. 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