Attractor scanner and 7P: A spatiotemporal fingerprint and an operational robustness score for low-dimensional chaos

We present a practical workflow for identifying and comparing chaotic regimes in low-dimensional continuous-time systems. The procedure combines four complementary elements: the largest Lyapunov exponent λmax as a fixed-protocol indicator of sensitive dependence, a local robustness score RCZ ∈ [0, 1] defined on a scanned two-parameter grid, an occupied phase-space footprint V = ΔxΔyΔz, and a fixed seven-panel (7P) spatiotemporal fingerprint. The 7P layout combines spatial and time–state projections, allowing differences in temporal organization, such as lobe dwelling, intermittent bursts, or basin hopping, to be inspected alongside geometric structure. Using the same numerical workflow without case-specific retuning, we illustrate the approach with four representative examples: the canonical Lorenz–63 attractor, a compact, bounded-chaotic Lorenz–63 regime at lower ρ, the classical Rössler spiral-with-bursts attractor, and a strongly anisotropic two-basin quadratic flow. For each case, we report λmax, RCZ, V, and the corresponding 7P fingerprint. Together, these quantities provide a compact comparative description of whether a regime exhibits chaos under the adopted protocol, how that chaos is organized in time, how extended it is in phase space, and how locally robust it is within the scanned parameter slice. The emphasis of the present work is methodological and comparative: a reproducible, easy-to-apply integration of established diagnostics with a fixed visualization protocol for side-by-side analysis of low-dimensional chaotic regimes.