Verification of chaotic behavior in an experimental loudspeaker

Abstract

The dynamics of an experimental electrodynamic loudspeaker is studied by using the tools of chaos theory and time series analysis. Delay time, embedding dimension, fractal dimension, and other empirical quantities are determined from experimental data. Particular attention is paid to issues of stationarity in a system in order to identify sources of uncertainty. Lyapunov exponents and fractal dimension are measured using several independent techniques. Results are compared in order to establish independent confirmation of low dimensional dynamics and a positive dominant Lyapunov exponent. We thus show that the loudspeaker may function as a chaotic system suitable for low dimensional modeling and the application of chaos control techniques.

Quantifying chaos: A tale of two maps

“…Yet examples abound in which Lyapunov exponent estimates are provided with neither of these two requirements confirmed (e.g. [3,4,5,6,7,8,9]). Some have emphasised the need to provide confidence limits along with the estimates [10,11], but confidence limits are valuable only when there is evidence of convergence.…”

Two Maps and Worldwide Ipod Interest

“…In forecasting, Lyapunov exponents are used to quantify how predictable the underlying system is (e. g. [1]). They can also be used to merely characterise the system as has been done in diagnostic studies (e. g. [2,3]). For these reasons, literature abounds in which numerical computations of Lyapunov exponents are sought with diverse applications.…”

“…It is therefore necessary to establish convergence before reporting any estimates; but there are many examples where convergence is, at the best, not adequately established (e.g. [1,2,3,6,7,8,9]). …”