{"paper":{"title":"Approximating the Amplitude and Form of Limit Cycles in the Weakly Nonlinear Regime of Lienard Systems","license":"","headline":"","cross_cats":["cs.DM","math.DS"],"primary_cat":"nlin.AO","authors_text":"Jose-Luis Lopez, Ricardo Lopez-Ruiz","submitted_at":"2006-03-31T16:59:28Z","abstract_excerpt":"Li\\'{e}nard equations, $\\ddot{x}+\\epsilon f(x)\\dot{x}+x=0$, with $f(x)$ an even continuous function are considered. In the weakly nonlinear regime ($\\epsilon\\to 0$), the number and an order zero in $\\epsilon$ approximation of the amplitude of limit cycles present in this type of systems can be obtained by applying a methodology recently proposed by the authors [L\\'opez-Ruiz R, L\\'opez JL. Bifurcation curves of limit cycles in some Li\\'enard systems. Int J Bifurcat Chaos 2000; 10:971-980]. In the present work, that method is carried forward to higher orders in $\\epsilon$ and is embedded in a ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0603076","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":""},"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"}