Three models of the whirling string through its route to chaos: run data and MATLAB code

Run data and MATLAB code for the paper "A comparison of three models of a whirling string as it becomes chaotic" (N. B. Tufillaro, 2026; submitted to Journal of Sound and Vibration). A stretched wire driven near its fundamental frequency can leave the plane of the driving force, whirl, and become chaotic. The paper compares three models of this motion: the geometrically exact string with both transverse polarizations and longitudinal motion, the two-mode Kirchhoff–Carrier equations, and Miles' averaged equations. It locates the Hopf bifurcation of the steady whirl, the period doubling and halving of the modulated whirl, and the primary Shil'nikov homoclinic orbit in all three, and measures how they shift with the small parameter ε = c/ω₁. The deposit contains:- the brute-force bifurcation scans of the three models at two dampings (γ = 0.45, 0.50) and seven values of σ;- the growth-rate runs near the Hopf point, the homoclinic-orbit runs (splitting function and unstable rate) and the kick runs for the saddle-focus spiral rate;- the Lyapunov-exponent sweeps and the long runs used for the return maps;- the MATLAB code for the three models (including a two-polarization extension of Ducceschi and Bilbao's energy-quadratised scheme for the geometrically exact string), the run jobs, and the scripts that produce every table and figure of the paper from the run files. README.md describes the layout, the file formats, the frequency-offset corrections, and the commands that reproduce Tables 1–4 and Figs. 3–7.