Wavelet Analysis of Chaotic Dynamical Systems.
Sei-ichi IIDA, Naoki Hagiwara, Kakuji OGAWARA · TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series B · 1993
A recent method "wavelet analysis" is applied as a tool for analyzing time sequential quantities derived from chaotic systems. As typical examples, the present method is applied to two well known systems, the Lorenz model and the Rossler model. The main procedure consists of calculating the local cross correlations between the signal to be analyzed and a predefined waveform called a "wavelet" at various time scales. This makes it possible to unfold the signal into both time and frequency, whereas in Fourier analysis, results are obtained in the frequency domain. The present paper mainly focuses on understanding the properties of this method, and shows a way to interpret the results.