Reconstructing attractors from scalar time series: A comparison of singular system and redundancy criteria

Abstract

A delay-vector phase space reconstruction in which the delay time satisfies a minimum redundan~ criterion is compared with a reconstruction obtained using a singular system approach, Minimum redundancy produces the better reconstruction. The reconstructions are compared using a distortion functional .~ which measures how well the location of a point in the original phase space can be determ~i~ed on the basis of its image under the reconstruction process. The superiority of the redundancy analysis over the singular system analysis ~s found to arise from the former's foundation on the notion of general independence as opposed to the latter's foundation on the notion of linear independence.

A Practical Method for the Measurements of the Chaoticity of Electric and Magnetic Brain Activity

“…The most frequently applied method is the first zero-crossing of autocorrelation function [Schuster, 1989]. Another method searches for the minimum in the mutual information [Fraser & Swinney, 1986;Fraser, 1989] (see also Graf & Elbert [1989] for an application to EEG, suggesting that it may be sufficient to consider the autocorrelation). Theoretically, for the infinite time series the choice of the delay-time is unimportant and the key role plays the choice of embedding dimension e. In practice, the measured signals are short and the choice of both parameters is critical.…”

Dynamics of thin-walled element milling expressed by recurrence analysis

“…The false nearest neighbours function (FNN) is based on searching for an m-dimensional state space in which there are no false crossings of the trajectories. More information about the AMI and the FNN functions can be found in [12,30]. In the present work, the Tisean software [15] is used to obtain the embedding parameters.…”

Nonlinear Analysis of Surface EMG Signals

“…It provides its convenience for the further analysis of the given system. Numerical experience, however, led several authors to express some doubts about reliability of singular system analysis in the attractor reconstruction [46][47][48]. Palus and Dvorak [37] explain why singular-value decomposition(SVD), the heart of the singular system analysis and by nature a linear method, may become misleading technique when it is used in nonlinear dynamics studies that reconstruction parameters are time-delay, embedding dimension (or embedding windows).…”