{"paper":{"title":"Global Centers and Phase Portraits in Generalized Duffing Oscillators: A Comprehensive Study of the Center-Focus Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Gabriel Rond\\'on, Nasrin Sadri","submitted_at":"2025-06-08T22:43:09Z","abstract_excerpt":"This work presents a comprehensive study of the generalized Duffing oscillator, a fundamental model in nonlinear dynamics described by the system $$ \\dot{x} = y, \\quad \\dot{y} = -\\alpha y - \\epsilon x^m - \\sigma x, $$ where $\\epsilon \\neq 0$ and $m \\geq 1$. We focus on the topological classification of phase portraits, the characterization of global centers, and the absence of limit cycles for $\\alpha\\neq0$. For the linear case ($m = 1$), we establish necessary and sufficient conditions for the origin to be a global center, showing that this occurs if, and only if, $\\alpha = 0$ and $\\epsilon +"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07307","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/2506.07307/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"}