EXPONENTIAL CHARACTERISTICS OF POWER SPECTRAL DENSITIES CAUSED BY CHAOTIC PHENOMENA

Power spectral densities (PSD's) were calculated by the maximum entropy method (MEM) for three types of chaotic rime series numerically generated from the Lorenz, Rossler and Duffing models. Every PSD indicated exponential decay until it levels off at a limit determined by the accuracy of the present computation. This exponential chracteristics were universally found in all chaotic time series irrespective of the data length as well as the time range of data. The values of the coefficient of exponent were 3.26, 5.72 and 7.36 for 6000-point data of the Lorenz, Rossler and Duffing models, respectively, and they slightly increased as the data length shortened. The exponential form was also recognized in the MEM-PSD for the Lorentzian-type time series as in theory.