Trajectory-Only Structural Regime Detection in Deterministic Dynamical Systems

Deterministic dynamical systems are often analyzed with model-aware diagnostics, but those methods do not answer a narrower question: can a regime-relevant boundary be identified when detection is restricted to trajectories alone? This study evaluates that question with a minimal, non-ML framework for trajectory-only structural regime detection from multivariate/full-state trajectories. The framework builds a trajectory-only indicator atlas, aggregates selected trajectory-derived indicators into a structural score, and extracts a structural boundary along an ordered parameter sweep. Model-aware or benchmark-specific diagnostics are kept separate in an oracle validation layer used only for post hoc evaluation through a qualitative boundary and the lead distance between boundaries. On the FitzHugh-Nagumo benchmark, the structural boundary occurs at 𝜖_struct = 0.1158 and the oracle-defined qualitative boundary at 𝜖_qual = 0.49719, giving a lead distance of 0.38139. On an autonomous forced van der Pol benchmark, the structural boundary occurs at 𝐴_struct = 1.025 and the qualitative boundary at 𝐴_qual = 1.25, giving a lead distance of 0.225. Core robustness, supplemental scalar-delay robustness, specificity, ablation, integrity, and contract checks all pass in the frozen paper suite. The main result is simple: on both tested systems, the structural boundary occurs before the oracle-defined qualitative boundary. This record contains the manuscript and supplementary notes. Code for the study is archived separately under DOI: 10.5281/zenodo.19465797. The active project repository, including code, outputs, and supplementary notes, is available at https://github.com/guptaaryanr/RegimeAtlas.