{"paper":{"title":"Small noise and long time phase diffusion in stochastic limit cycle oscillators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DS","math.MP","q-bio.QM"],"primary_cat":"math.PR","authors_text":"Assaf Shapira, Christophe Poquet, Giambattista Giacomin","submitted_at":"2015-12-14T18:06:53Z","abstract_excerpt":"We study the effect of additive Brownian noise on an ODE system that has a stable hyperbolic limit cycle, for initial data that are attracted to the limit cycle. The analysis is performed in the limit of small noise - that is, we modulate the noise by a factor $\\varepsilon \\searrow 0$ - and on a long time horizon. We prove explicit estimates on the proximity of the noisy trajectory and the limit cycle up to times $\\exp\\left(c \\varepsilon^{-2}\\right)$, $c>0$, and we show both that on the time scale $\\varepsilon^{-2}$ the \"'dephasing\" (i.e., the difference between noiseless and noisy system meas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04436","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"}