{"paper":{"title":"Slow-fast dynamics in a planar parasite--host model with an extinction singularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Hildeberto Jard\\'on-Kojakhmetov, Jacopo Borsotti, Mattia Sensi","submitted_at":"2026-02-22T16:14:57Z","abstract_excerpt":"We study a slow-fast parasite--host model featuring a singularity at the extinction state. Using techniques from Geometric Singular Perturbation Theory (GSPT), and in particular the so-called blow-up method, we desingularize that point and reconstruct the local and global dynamics. The system we consider is in non-standard GSPT form and is characterized by a rich dynamical behavior: families of slow-fast homoclinic orbits, canard-like transitions generated by trajectories that remain close to a repelling critical manifold, and topological changes produced by infinitesimal variations of the inf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.19257","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.19257/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"}