{"paper":{"title":"Pattern Formation on Networks: from Localised Activity to Turing Patterns","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DS","math.MP","nlin.PS"],"primary_cat":"nlin.AO","authors_text":"Nick McCullen, Thomas Wagenknecht","submitted_at":"2016-01-20T20:44:01Z","abstract_excerpt":"Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\\em random} networks. Understanding how patterns of activity arise in such systems is important for understanding many natural phenomena. The emergence of patterns of activity on complex networks with reaction-diffusion dynamics on the nodes is studied here. The connection between solutions with a single activated node, which can bifurcate from an undifferentiated state, and the fully developed system-scale patterns are investigated computationally. The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05404","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"}