{"paper":{"title":"Selection of the angular speed of rotating waves in segregated reaction-diffusion systems with asymmetric competition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessandro Zilio, Gianmaria Verzini, Giuseppe Spadaro","submitted_at":"2026-06-26T15:52:39Z","abstract_excerpt":"We investigate the existence of segregated rotating waves, arising in the singular limit of competition-diffusion systems of the type \\[ \\partial_t u_i -\\partial_{xx} u_i = f(u_i)-\\beta u_i \\sum_{j \\neq i} a_{ij} u_j,\\qquad x\\in\\mathbb{S}^1,\\ t>0, 1\\le i,j\\le k, \\] as $\\beta\\to+\\infty$. Here $k\\ge3$, the reaction $f$ is of Fisher-KPP (logistic) type, and the competition coefficients $a_{ij}>0$ are not necessarily symmetric. Assuming that, for every $i$, \\[ \\dfrac{a_{i+1,i}}{a_{i,i+1}}=\\lambda>0, \\] we provide a complete characterization of the rotating waves enjoying an equivariant structure, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28203","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.28203/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}