Neutral Entry–Exit Cycles with Quadratic Grazing: Uniform Return Reduction and Local Two-Parameter Bifurcations

Abstract

Version 1.4.0 of the research materials for “Neutral Entry–Exit Cycles with Quadratic Grazing: Uniform Return Reduction and Local Two-Parameter Bifurcations” (arXiv:2607.27464). The primary record file is neutral-entry-exit-arxiv.pdf (43 pages, 3 figures) and is selected for direct PDF preview. The curated reproducibility archive contains the manuscript source, dual-backend interval certificates, a CAPD validated-ODE certificate, separately labelled positive-parameter numerical material, machine-readable results, and reproduction instructions. Journal-submission materials are excluded. The work derives the positive-parameter physical Poincare displacement for a separated entry–exit and quadratic-grazing circuit, constructs the complete marked local two-parameter bifurcation diagram, and classifies cycle number, itinerary, and stability. The open chambers contain zero or two cycles when the smooth and grazing coefficients have the same sign, and one or three when their signs are opposite. A compact polynomial family realizes both sign classes, while a cutoff-Gause family transfers the diagram to explicit response parameters. Repository: https://github.com/h-lu/tangent-entry-exit-topicSource commit: 34f4429a6097bbd64ed20b2225a0de4454e2e844Standalone PDF SHA-256: ff3f735212afa9ed778572636fc9f54c47353f4d3e527eee25552494767619d3Reproducibility archive SHA-256: 37b8b390a66c48e5abd9a137c1007d17dae2b82134338f10b13d62ec33f2b8ddManifest SHA-256: aee67a0c0813b22ff7d51dada09c8b6d804c4b9baa8591f907155fd94c32675f