{"paper":{"title":"Variational approach to a class of nonlinear oscillators with several limit cycles","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"J. Mura, M. C. Depassier","submitted_at":"2001-03-22T17:07:08Z","abstract_excerpt":"We study limit cycles of nonlinear oscillators described by the equation\n $\\ddot x + \\nu F(\\dot x) + x =0$. Depending on the nonlinearity this equation may exhibit different number of limit cycles.\n We show that limit cycles correspond to relative extrema of a certain functional. Analytical results in the limits $\\nu ->0$ and $\\nu -> \\infty$ are in agreement with previously known criteria. For intermediate $\\nu$ numerical determination of the limit cycles can be obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0103034","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"}