{"paper":{"title":"Probabilistic response and rare events in Mathieu's equation under correlated parametric excitation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.data-an"],"primary_cat":"math.DS","authors_text":"Mustafa A. Mohamad, Themistoklis P. Sapsis","submitted_at":"2017-05-31T22:05:34Z","abstract_excerpt":"We derive an analytical approximation to the probability distribution function (pdf) for the response of Mathieu's equation under parametric excitation by a random process with a spectrum peaked at the main resonant frequency, motivated by the problem of large amplitude ship roll resonance in random seas. The inclusion of random stochastic excitation renders the otherwise straightforward response to a system undergoing intermittent resonances: randomly occurring large amplitude bursts. Intermittent resonance occurs precisely when the random parametric excitation pushes the system into the inst"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00109","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"}