Chaos parameters for EEG analysis

The possibility to apply nonlinear dynamics methods for the EEG time series analysis is investigated. Problems related with the estimation of the chaos parameters from the physiological data are discussed

Asymptotic power law of moments in a random multiplicative process with weak additive noise

It is well known that a random multiplicative process with weak additive noise generates a power-law probability distribution. It has recently been recognized that this process exhibits another type of power law: the moment of the stochastic variable scales as a function of the additive noise strength. We clarify the mechanism for this power-law behavior of moments by treating a simple Langevin-type model both approximately and exactly, and argue this mechanism is universal. We also discuss the relevance of our findings to noisy on-off intermittency and to singular spatio-temporal chaos recently observed in systems of non-locally coupled elements.Comment: 11 pages, 9 figures, submitted to Phys. Rev.

Effects of the low frequencies of noise on On-Off intermittency

A bifurcating system subject to multiplicative noise can exhibit on-off intermittency close to the instability threshold. For a canonical system, we discuss the dependence of this intermittency on the Power Spectrum Density (PSD) of the noise. Our study is based on the calculation of the Probability Density Function (PDF) of the unstable variable. We derive analytical results for some particular types of noises and interpret them in the framework of on-off intermittency. Besides, we perform a cumulant expansion for a random noise with arbitrary power spectrum density and show that the intermittent regime is controlled by the ratio between the departure from the threshold and the value of the PSD of the noise at zero frequency. Our results are in agreement with numerical simulations performed with two types of random perturbations: colored Gaussian noise and deterministic fluctuations of a chaotic variable. Extensions of this study to another, more complex, system are presented and the underlying mechanisms are discussed.Comment: 13pages, 13 figure

Don't bleach chaotic data

A common first step in time series signal analysis involves digitally filtering the data to remove linear correlations. The residual data is spectrally white (it is ``bleached''), but in principle retains the nonlinear structure of the original time series. It is well known that simple linear autocorrelation can give rise to spurious results in algorithms for estimating nonlinear invariants, such as fractal dimension and Lyapunov exponents. In theory, bleached data avoids these pitfalls. But in practice, bleaching obscures the underlying deterministic structure of a low-dimensional chaotic process. This appears to be a property of the chaos itself, since nonchaotic data are not similarly affected. The adverse effects of bleaching are demonstrated in a series of numerical experiments on known chaotic data. Some theoretical aspects are also discussed.Comment: 12 dense pages (82K) of ordinary LaTeX; uses macro psfig.tex for inclusion of figures in text; figures are uufile'd into a single file of size 306K; the final dvips'd postscript file is about 1.3mb Replaced 9/30/93 to incorporate final changes in the proofs and to make the LaTeX more portable; the paper will appear in CHAOS 4 (Dec, 1993

Independent Component Analysis of Spatiotemporal Chaos

Two types of spatiotemporal chaos exhibited by ensembles of coupled nonlinear oscillators are analyzed using independent component analysis (ICA). For diffusively coupled complex Ginzburg-Landau oscillators that exhibit smooth amplitude patterns, ICA extracts localized one-humped basis vectors that reflect the characteristic hole structures of the system, and for nonlocally coupled complex Ginzburg-Landau oscillators with fractal amplitude patterns, ICA extracts localized basis vectors with characteristic gap structures. Statistics of the decomposed signals also provide insight into the complex dynamics of the spatiotemporal chaos.Comment: 5 pages, 6 figures, JPSJ Vol 74, No.

Fundamental scaling laws of on-off intermittency in a stochastically driven dissipative pattern forming system

Noise driven electroconvection in sandwich cells of nematic liquid crystals exhibits on-off intermittent behaviour at the onset of the instability. We study laser scattering of convection rolls to characterize the wavelengths and the trajectories of the stochastic amplitudes of the intermittent structures. The pattern wavelengths and the statistics of these trajectories are in quantitative agreement with simulations of the linearized electrohydrodynamic equations. The fundamental $\tau^{-3/2}$ distribution law for the durations $\tau$ of laminar phases as well as the power law of the amplitude distribution of intermittent bursts are confirmed in the experiments. Power spectral densities of the experimental and numerically simulated trajectories are discussed.Comment: 20 pages and 17 figure

Correlation in the heart rate data

Variety of methods of nonlinear dynamics have been used for possibility of an analysis of time series in experimental physiology. Dynamical nature of experimental data was checked using specific methods. Statistical properties of the heart rate have been investigated. Correlation between of cardiovascular function and statistical properties of both, heart rate and stroke volume, have been analyzed. Possibility to use a data from correlations in heart rate for monitoring of cardiovascular function was discussed