{"paper":{"title":"Signature stability analysis for networks of coupled dynamical systems with Hermitian Jacobian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.AO"],"primary_cat":"math.DS","authors_text":"Anne-Ly Do, Jeremias Epperlein, Stefano Boccaletti, Stefan Siegmund, Thilo gross","submitted_at":"2012-07-24T13:44:34Z","abstract_excerpt":"The central theme of complex systems research is understanding the emergent macroscopic properties of a system from the interplay of its microscopic constituents. Here, we ask what conditions a complex network of microscopic dynamical units has to meet to permit stationary macroscopic dynamics, such as stable equilibria or phase-locked states. We present an analytical approach which is based on a graphical notation that allows rewriting Jacobi's signature criterion in an interpretable form. The derived conditions pertain to topological structures on all scales, ranging from individual nodes to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5699","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"}