Detecting Determinism in High Dimensional Chaotic Systems

A method based upon the statistical evaluation of the differentiability of the measure along the trajectory is used to identify in high dimensional systems. The results show that the method is suitable for discriminating stochastic from deterministic systems even if the dimension of the latter is as high as 13. The method is shown to succeed in identifying determinism in electro-encephalogram signals simulated by means of a high dimensional system.Comment: 8 pages (RevTeX 3 style), 5 EPS figures, submitted to Phys. Rev. E (25 apr 2001

Extended Recurrence Plot Analysis and its Application to ERP Data

We present new measures of complexity and their application to event related potential data. The new measures base on structures of recurrence plots and makes the identification of chaos-chaos transitions possible. The application of these measures to data from single-trials of the Oddball experiment can identify laminar states therein. This offers a new way of analyzing event-related activity on a single-trial basis.Comment: 21 pages, 8 figures; article for the workshop ''Analyzing and Modelling Event-Related Brain Potentials: Cognitive and Neural Approaches`` at November 29 - December 01, 2001 in Potsdam, German

How to avoid potential pitfalls in recurrence plot based data analysis

Recurrence plots and recurrence quantification analysis have become popular in the last two decades. Recurrence based methods have on the one hand a deep foundation in the theory of dynamical systems and are on the other hand powerful tools for the investigation of a variety of problems. The increasing interest encompasses the growing risk of misuse and uncritical application of these methods. Therefore, we point out potential problems and pitfalls related to different aspects of the application of recurrence plots and recurrence quantification analysis

Nonlinear dynamical analysis of brain electrical activity due to exposure to weak environmentally relevant electromagnetic fields

The reports dealing with the effects of weak electromagnetic fields (EMFs) on brain electrical activity have been inconsistent. We suspected that the use of linear models and their associated methods accounted for some of the variability, and we explored the issue by using a novel approach to study the effects of EMFs on the electroencephalogram (EEG) from rabbits and humans. The EEG was embedded in phase space and local recurrence plots were calculated and quantified to permit comparisons between exposed and control epochs from individual subjects. Statistically significant alterations in brain activity were observed in each subject when exposed to weak EMFs, as assessed using each of two recurrence-plot quantifiers. Each result was replicated; a sham exposure control procedure ruled out the possibility that the effect of the field was a product of the method of analysis. No differences were found between exposed and control epochs in any animal when the experiment was repeated after the rabbits had been killed, indicating that a putative interaction between the field and the EEG electrodes could not account for the observed effects. We conclude that EMF transduction resulting in changes in brain electrical activity could be demonstrated consistently using methods derived from nonlinear dynamical systems theory

Interdisciplinary application of nonlinear time series methods

This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely deterministic and the potential that remains in this situation is discussed. For signals with weakly nonlinear structure, the presence of nonlinearity in a general sense has to be inferred statistically. The paper reviews the relevant methods and discusses the implications for deterministic modeling. Most field measurements yield nonstationary time series, which poses a severe problem for their analysis. Recent progress in the detection and understanding of nonstationarity is reported. If a clear signature of approximate determinism is found, the notions of phase space, attractors, invariant manifolds etc. provide a convenient framework for time series analysis. Although the results have to be interpreted with great care, superior performance can be achieved for typical signal processing tasks. In particular, prediction and filtering of signals are discussed, as well as the classification of system states by means of time series recordings.Comment: 86 pages, 26 figure

A Novel Approach For Detection of Neurological Disorders through Electrical Potential Developed in Brain

This paper talks about the phenomenon of recurrence and using this concept it proposes a novel and a very simple and user friendly method to diagnose the neurological disorders by using the EEG signals.The mathematical concept of recurrence forms the basis for the detection of neurological disorders,and the tool used is MATLAB.  Using MATLAB, an algorithm is designed which uses EEG signals as the input and uses the synchronizing patterns of EEG signals to determine various neurological disorders through graphs and recurrence plot