Biomedical subjects

Wiesław M Macek

Publications and source records attributed to Wiesław M Macek.

3 recordsLinked to original sources

PubMed2005

Discriminating additive from dynamical noise for chaotic time series.

We consider the dynamics of the Hénon and Ikeda maps in the presence of additive and dynamical noise. We show that, from the point of view of computations of some statistical quantities, dynamical noise corrupting these deterministic systems can be considered effectively as an additive "pseudonoise" with the Cauchy distribution. In the case of the Hénon and Ikeda maps, this effect occurs only for one variable of the system, while the noise corrupting the second variable is still Gaussian distributed independent of distribution of dynamical noise. Based on these results and using scaling properties of the correlation entropy, we propose a simple method of discriminating additive from dynamical noise. This approach is also useful for estimation of noise level for chaotic time series. We show that the proposed method works well in a wide range of noise levels, providing that one kind of noise predominates and we analyze the variable of the system for which the contamination follows Cauchy-like distribution in the presence of dynamical noise.

Journal Article↗

PubMed2005

Generalized dimensions for fluctuations in the solar wind.

We analyze time series of velocities of the solar wind plasma including the outward-directed component of Alfvénic turbulence within slow wind observed by the Helios 2 spacecraft in the inner heliosphere. We demonstrate that the influence of noise in the data can be efficiently reduced by a singular-value decomposition filter. The resulting generalized dimensions show a multifractal structure of the solar wind attractor in the inner heliosphere. The obtained multifractal spectrum is consistent with that for the multifractal measure on the self-similar weighted baker's map with two parameters describing uniform compression and natural invariant measure on the attractor of the system.

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PubMed2002

Influence of colored noise on chaotic systems.

We focus on classical chaotic systems corrupted by white and colored noise. We study the dependence of the correlation dimension and the Kolmogorov entropy on the noise level and its spectral exponent. As is well known, white noise strongly reduces the width of the scaling region for the correlation dimension and entropy. On the contrary, we demonstrate that colored noise does not basically obscure the scaling region, changing only the shape of the correlation sum for length scales smaller than the noise level. The numerical results show that, even for a noise level as high as approximately 5%, a reasonably wide plateau for the correlation sum is still obtained, but the value of the calculated dimension is somewhat increased. The calculated correlation dimension is a bilinear function of the noise level and the dimension of the noise, which depends on the spectral exponent of the noise. On the other hand, the width of the scaling region for the correlation entropy depends on this spectral exponent, but the value of the plateau does not change substantially.

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