{"paper":{"title":"Hyperbolic Geometry of Kuramoto Oscillator Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math.DS"],"primary_cat":"nlin.AO","authors_text":"Bolun Chen, Jan R. Engelbrecht, Renato Mirollo","submitted_at":"2017-07-03T18:08:54Z","abstract_excerpt":"Kuramoto oscillator networks have the special property that their trajectories are constrained to lie on the (at most) 3D orbits of the M\\\"obius group acting on the state space $T^N$ (the $N$-fold torus). This result has been used to explain the existence of the $N-3$ constants of motion discovered by Watanabe and Strogatz for Kuramoto oscillator networks. In this work we investigate geometric consequences of this M\\\"obius group action. The dynamics of Kuramoto phase models can be further reduced to 2D reduced group orbits, which have a natural geometry equivalent to the unit disk $\\Delta$ wit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.00713","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":""},"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"}