{"paper":{"title":"Convergence to the Equilibrium in a Lotka-Volterra Ode Competition System with Mutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.PE"],"primary_cat":"math.AP","authors_text":"Frederic Fabre, Jerome Coville (BIOSP)","submitted_at":"2013-01-26T11:17:55Z","abstract_excerpt":"In this paper we are investigating the long time behaviour of the solution of a mutation competition model of Lotka-Volterra's type. Our main motivation comes from the analysis of the Lotka-Volterra's competition system with mutation which simulates the demo-genetic dynamics of diverse virus in their host : $$ \\frac{dv_{i}(t)}{dt}=v_i\\[r_i-\\frac{1}{K}\\Psi_i(v)\\]+\\sum_{j=1}^{N} \\mu_{ij}(v_j-v_i). $$ In a first part we analyse the case where the competition terms $\\Psi_i$ are independent of the virus type $i$. In this situation and under some rather general assumptions on the functions $\\Psi_i$,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6237","kind":"arxiv","version":2},"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"}