{"paper":{"title":"Global and Local: Synchronization and Emergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Leo P. Kadanoff, Mogens H. Jensen","submitted_at":"2012-01-02T14:55:24Z","abstract_excerpt":"When a dynamical system contains several different modes of oscillations it may behave in a variety of ways: If the modes oscillate at their own individual frequencies, it exhibits quasiperiodic behavior; when the modes lock to one another it becomes synchronized, or, as a third possibility, complex chaotic behavior may emerge. With two modes present, like an internal oscillation coupled to a periodic external signal, one obtains a highly structured phase diagram that exhibits these possibilities. In essence, the details are related to the difference between rational and irrational numbers. Na"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0476","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"}