{"paper":{"title":"Analysis of a remarkable singularity in a nonlinear DDE","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.CD"],"primary_cat":"math.DS","authors_text":"B. Shayak, Matthew Davidow, Richard H. Rand","submitted_at":"2017-01-01T05:27:10Z","abstract_excerpt":"In this work we investigate the dynamics of the nonlinear DDE (delay-differential equation)\n  x''(t)+x(t-T)+x(t)^3=0\n  where T is the delay. For T=0 this system is conservative and exhibits no limit cycles. For T>0, no matter how small, an infinite number of limit cycles exist, their amplitudes going to infinity in the limit as T approaches zero.\n  We investigate this situation in three ways: 1) Harmonic Balance, 2) Melnikov's integral, and 3) Adding damping to regularize the singularity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.00201","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"}