Correlation dimensions in various parts of cat and human brain in different states

The analysis of deterministic chaos is currently an active field in many branches of research. Mathematically, all nonlinear dynamical systems with more than two degrees of freedom can generate chaos and, therefore, become unpredictable over a longer time scale. In order to describe periodic, aperiodic, or even chaotic behavior of nonlinear systems, several approaches have been used. In 1963 Lorenz applied concepts of nonlinear dynamics to the convection phenomenon in hydrodynamics in order to describe atmospheric turbulence (Navier-Stokes equation). He demonstrated the possibility that the unpredictable or chaotic behavior observed in an infinite-dimensional system might be caused by a three-dimensional dynamical system. Our research group’s first nonlinear approach consisted in comparing the relation between EEG and evoked potentials by considering the Duffing equation as an adequate nonlinear model (Basar 1980). Later, assuming the EEG to be a chaotic attractor and mentioning the possibilities of applying the Navier-Stokes equation for comparison, we described that the EEG might reflect properties of a strange attractor (Basar 1983; Basar and Roschke 1983).