EXPONENTIAL CHARACTERISTICS OF POWER SPECTRAL DENSITIES CAUSED BY CHAOTIC PHENOMENA

Power spectral densities (PSD's) were calculated by the maximum entrop y method (MEM) for three types of chaotic rime series numerically gene rated from the Lorenz, Rossler and Duffing models. Every PSD indicated exponential decay until it levels off at a limit determined by the ac curacy of the present computation. This exponential chracteristics wer e universally found in all chaotic time series irrespective of the dat a length as well as the time range of data. The values of the coeffici ent of exponent were 3.26, 5.72 and 7.36 for 6000-point data of the Lo renz, Rossler and Duffing models, respectively, and they slightly incr eased as the data length shortened. The exponential form was also reco gnized in the MEM-PSD for the Lorentzian-type time series as in theory .