{"paper":{"title":"Vibration of the Duffing Oscillator: Effect of Fractional Damping","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Arkadiusz Syta, Grzegorz Litak, Marek Borowiec","submitted_at":"2006-01-14T16:34:00Z","abstract_excerpt":"We have applied the Melnikov criterion to examine a global homoclinic bifurcation and transition to chaos in a case of the Duffing system with nonlinear fractional damping and external excitation.\n Using perturbation methods we have found a critical forcing amplitude above which the system may behave chaotically.\n The results have been verified by numerical simulations using standard nonlinear tools as\n Poincare maps and a Lyapunov exponent. Above the critical Melnikov amplitude $\\mu_c$, which is the sufficient condition of a global homoclinic bifurcation, we have observed the region with a tr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0601033","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"}