{"paper":{"title":"Controlling transitions in a Duffing oscillator by sweeping parameters in time","license":"","headline":"","cross_cats":[],"primary_cat":"nlin.AO","authors_text":"Oleg Kogan","submitted_at":"2006-07-13T01:08:52Z","abstract_excerpt":"We consider a high-$Q$ Duffing oscillator in a weakly non-linear regime with the driving frequency $\\sigma$ varying in time between $\\sigma_i$ and $\\sigma_f$ at a characteristic rate $r$. We found that the frequency sweep can cause controlled transitions between two stable states of the system. Moreover, these transitions are accomplished via a transient that lingers for a long time around the third, unstable fixed point of saddle type. We propose a simple explanation for this phenomenon and find the transient life-time to scale as $-(\\ln{|r-r_c|})/\\lambda_r$ where $r_c$ is the critical rate n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0607023","kind":"arxiv","version":2},"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"}