{"paper":{"title":"The Infinitesimal Phase Response Curves of Oscillators in Piecewise Smooth Dynamical Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Hillel J. Chiel, Kendrick M. Shaw, Peter J. Thomas, Youngmin Park","submitted_at":"2016-03-11T02:26:12Z","abstract_excerpt":"The asymptotic phase $\\theta$ of an initial point $x$ in the stable manifold of a limit cycle identifies the phase of the point on the limit cycle to which the flow $\\phi_t(x)$ converges as $t\\to\\infty$. The infinitesimal phase response curve (iPRC) quantifies the change in timing due to a small perturbation of a limit cycle trajectory. For a stable limit cycle in a smooth dynamical system the iPRC is the gradient $\\nabla_x(\\theta)$ of the phase function, which can be obtained via the adjoint of the variational equation. For systems with discontinuous dynamics, the standard approach to obtaini"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.03503","kind":"arxiv","version":3},"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"}