{"paper":{"title":"Phase Transitions in Systems of Interacting Species","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-bio.PE","authors_text":"Birger Bergersen, Margarita Ifti","submitted_at":"2014-03-11T07:13:17Z","abstract_excerpt":"We discuss an autocatalytic reaction system: the cyclic competition model A1 + A2 --> 2 A2, A2 + A3 --> 2 A3, A3 + A4 --> 2 A4, A4 + A1 --> 2 A1), as well as its neutral counterpart. Migrations are introduced into the model. When stochastic phenomena are taken into account, a phase transition between a ``fixation'' and a ``neutral'' regime is observed. In the ``fixation'' regime, species A1 and A3 form an alliance against species A2 and A4, and the final state is one in which one of the symbiotic pairs has won. The odd--even ``coarse--grained'' systems is mapped onto the two--species neutral ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2488","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"}