{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:46:04Z","timestamp":1760060764400,"version":"build-2065373602"},"reference-count":49,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,9,17]],"date-time":"2025-09-17T00:00:00Z","timestamp":1758067200000},"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":["71571091","71771112"],"award-info":[{"award-number":["71571091","71771112"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Collective intelligence systems have demonstrated considerable potential in dynamic adversarial environments due to their distributed, self-organizing, and highly robust characteristics. The crux of an efficacious defense lies in establishing a dynamically adjustable, non-uniform defense structure through the differentiation of internal member roles. The proposed model is a heterogeneous-swarm adaptive-defense model based on symmetry breaking and skin effect. The model draws from symmetry theory, incorporating the skin effect of conductor currents and the hierarchical structural characteristics of biological groups, such as starlings. The construction of a radially symmetric dynamic hierarchical swarm structure is achieved by assigning different types of individuals with distinct safety radius preferences. Secondly, the principle of symmetry breaking is employed to establish a phase transition mechanism from radial symmetry to directed defense, thereby achieving an adaptive barrier formation algorithm. This algorithm enables the defensive group to assess threat characteristics and dynamically adjust defense resource deployment. The simulation results obtained from this study validate the phase transition process from continuous rotational symmetry to directed defense. This process demonstrates the barrier formation mechanism and ensures the safety and integrity of the core units within the group.<\/jats:p>","DOI":"10.3390\/sym17091555","type":"journal-article","created":{"date-parts":[[2025,9,17]],"date-time":"2025-09-17T11:00:00Z","timestamp":1758106800000},"page":"1555","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Heterogeneous Group Adaptive Defense Model Based on Symmetry-Breaking and Skin Effect"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-2250-2530","authenticated-orcid":false,"given":"Yunzhuo","family":"Ma","sequence":"first","affiliation":[{"name":"School of Electronic and Information Engineering, University of Science and Technology Liaoning, Anshan 114051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peng","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Intelligent Equipment Engineering, Wuxi Taihu University, Wuxi 214064, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Meijuan","family":"Li","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, University of Science and Technology Liaoning, Anshan 114051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6799-7667","authenticated-orcid":false,"given":"Xue-Bo","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, University of Science and Technology Liaoning, Anshan 114051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.physrep.2012.03.004","article-title":"Collective motion","volume":"517","author":"Vicsek","year":"2012","journal-title":"Phys. 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