Dresden 2003 – scientific programme

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DY: Dynamik und Statistische Physik

DY 42: Synchronisation I

DY 42.1: Talk

Thursday, March 27, 2003, 11:00–11:15, G\"OR/226

Influence of noise on the dynamics with fractal power spectra — •Michael Zaks — Lehrstuhl für Stochastische Prozesse, Humboldt Universität zu Berlin

In deterministic dynamics, the place of processes with fractal (singular-continuous) Fourier spectra is between the ordered and the chaotic behavior. Such processes have been found to occur both in the phase space of low-dimensional systems and in the physical space: along the streamlines of steady plane flows of viscous fluids through the periodic arrays of stationary vortices or past the lattices of solid bodies. We investigate how different kinds of noise affect these processes.

In general, under the influence of noise the spectral measure becomes absolutely continuous, and the correlations decay. However, during the certain transition phase the autocorrelation corresponds to the typical patterns of dynamics with fractal spectra. It turns out that the length of this phase is connected to the noise intensity by means of the power law. In symbolic sequences with fractal spectral properties the long-range correlations can persist in spite of the presence of noise.