Practical Evaluation of Invariant Measures for the Chaotic Response of a Two-Frequency Excited Mechanical Oscillator

Abstract

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