{"paper":{"title":"FitzHugh-Nagumo equation: bifurcations, slow-fast system and dynamics near infinity","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alexandre A. P. Rodrigues, Nasrin Sadri","submitted_at":"2025-07-02T11:52:39Z","abstract_excerpt":"In this paper, we present a qualitative and bifurcation analysis of the three-parameter FitzHugh-Nagumo system and its compactified formulation. The study is structured according to three parameter-dependent regimes, for which the associated phase portraits are characterized.\n  In one of these regimes, the system exhibits a double-zero bifurcation with $Z_2$ symmetry, corresponding to a codimension-two degeneracy. We compute explicit bifurcation and transition curves arising in the unfolding of this singularity, including pitchfork, Hopf, Belyakov, and double homoclinic bifurcations, and we co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.01623","kind":"arxiv","version":4},"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/2507.01623/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"}