{"paper":{"title":"Stabilized rapid oscillations in a delay equation: Feedback control by a small resonant delay","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bernold Fiedler, Isabelle Schneider","submitted_at":"2017-08-27T16:22:22Z","abstract_excerpt":"We study scalar delay equations $$\\dot{x} (t) = \\lambda f(x(t-1)) + b^{-1} (x(t) + x(t -p/2))$$ with odd nonlinearity $f$, real nonzero parameters $\\lambda, \\, b$, and two positive time delays $1,\\ p/2$. We assume supercritical Hopf~bifurcation from $x \\equiv 0$ in the well-understood single-delay case $b = \\infty$. Normalizing $f' (0)=1$, branches of constant minimal period $p_k = 2\\pi/\\omega_k$ are known to bifurcate from eigenvalues $i\\omega_k = i(k+\\tfrac{1}{2})\\pi$ at $\\lambda_k = (-1)^{k+1}\\omega_k$, for any nonnegative integer $k$. The unstable dimension of these rapidly oscillating per"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.08101","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"}