A Detailed Study of Power Spectral Density for Rossler System

Power spectral densities (PSD's) calculated by the maximum entropy method (MEM) for Rossler system indicated exponential decay with a large number of well-defined spectral lines. The spectral lines were confirmed to indicate a complete bifurcation up to the fifth-order period-doubling. An extremely anomalous behavior was recognized in the region of c =4.18–4.21 which is considered to be a transition region. The contribution of the power of the fundamental mode to the total power was overwhelmingly large: it becomes larger than 90%. A prediction of time series including chaotic ones was performed and the satisfactory results obtained. It will be discussed that the fluctuations due to amplitude instability of time series in the periodic solutions generate, resulting in the continuous component of PSD structured through the subharmonic cascade process, and this continuous region is restructured in the inverse cascade process (the socalled broad continuum in the chaotic mixing).