Influence of noise on dynamics with fractal Fourier spectra

In deterministic dynamics, the processes with fractal power spectra occupy the intermediate position between ordered and chaotic temporal behavior. We study numerically the influence of different kinds of noise upon these processes. In general, under the action of noise the spectral measure becomes absolutely continuous and the correlations decay. However, during the certain intermediate period the autocorrelation retains the pattern which is typical for dynamics with fractal spectra. Duration of this period is related to the noise intensity by the power law.