{"paper":{"title":"Complex systems in Ecology: a guided tour with large Lotka-Volterra models and random matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"q-bio.PE","authors_text":"Fran\\c{c}ois Massol, Imane Akjouj, Jamal Najim, Matthieu Barbier, Maxime Clenet, Myl\\`ene Ma\\\"ida, Viet Chi Tran, Walid Hachem","submitted_at":"2022-12-12T18:59:57Z","abstract_excerpt":"Ecosystems represent archetypal complex dynamical systems, often modelled by coupled differential equations of the form $$ \\frac{d x_i}{d t} = x_i \\varphi_i(x_1,\\cdots, x_N)\\ , $$ where $N$ represents the number of species and $x_i$, the abundance of species $i$. Among these families of coupled diffential equations, Lotka-Volterra (LV) equations $$ \\frac{d x_i}{d t} = x_i ( r_i - x_i +(\\Gamma \\mathbf{x})_i)\\ , $$ play a privileged role, as the LV model represents an acceptable trade-off between complexity and tractability. Here, $r_i$ represents the intrinsic growth of species $i$ and $\\Gamma$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.06136","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2212.06136/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}