Practical evaluation of invariant measures for the chaotic response of a two-frequency excited mechanical oscillator

This paper presents results which characterize the chaotic response of a low-dimensional mechanical oscillator. An experimental system based on a cart rolling on a two-well potential surface has been shown to closely approximate a modified form of Duffing's equation. Two-frequency forcing is applied, providing a useful means of varying the dimension of the response. Computation of correlation dimension and Lyapunov spectra are performed on both experimental and numerical data in order to assess the utility of these measures in a practical setting. A specific focus is the distinction between subharmonic and quasi-periodic forcing, since this has a subtle, and interesting, effect on the subsequent dynamics. The results tend to highlight the statistical nature of the measures and the caution that should be used in their interpretation.