Chaotic Dynamics in Brain Activity
The aim of this paper is to report on a new attempt at characterizing the electroencephalogram (EEG), which is based on recent progress in the theory of nonlinear dynamical systems (Brandstäter et al. 1983; Nicolis and Nicolis 1984, 1986; Babloyantz et al. 1985). The method is independent of any modeling of brain activity. It relies solely on the analysis of data obtained from a single-variable time series. From such a “one-dimensional” view of the system, one reconstructs the X k (where k = 1,…, n) variables necessary for the description of systems dynamics. With the help of these variables, phase-space trajectories are drawn. Provided that the dynamics of the system can be reduced to a set of deterministic laws, the system reaches in time a state of permanent regime. This fact is reflected by the convergence of families of phase trajectories toward a subset of the phase space. This invariant subset is called an “attractor.”
KeywordsPhase Space Brain Activity Phase Portrait Chaotic Dynamics Hausdorff Dimension
Unable to display preview. Download preview PDF.
- Berge P, Pomeau Y, Vidal C (1984) L’ordre dans le chaos: vers une approche déterministe de la turbulence. Hermann, ParisGoogle Scholar
- Grassberger P, Procaccia I (1983b) Measuring the strangeness of strange attractors. Physica [D] 9:189–208Google Scholar
- Wolf A, Swift JB, Swinney HL, Vastano JA (1985) Determining Lyapunov exponents from a time series. Physica [D] 16:285–317Google Scholar