A method of analysis for the extraction of inherent deterministic dependencies in a time series, recently developed by Savit and Green, is applied for the first time to EEG data. The defined indices d m () measure, within an uncertainty , the extent to which the i th element in a time series is a deterministic function of the j th element, with m = i-j. The estimation of these indices is based on conditional probabilities among the vectors in the phase space, a space that is reconstructed from the original time series with the method of delays. The required conditional probabilities are derived from the search for substrings of data of similar structure over the entire phase space. Therefore, the d m indices indicate global averages of the existing dependencies in a time series. The method has been proven very successful in detecting deterministic dependencies in the chaotic regime in a number of mathematical examples including the logistic, tent, and Henon maps, as well as the Lo...

The topic of this presentation is the investigation of the epileptic human brain as a nonlinear system that undergoes a phase transition (epileptic seizure). The estimated values of the largest Lyapunov exponent L over time indicated a more chaotic state postictally than ictally or preictally. The start of a seizure corresponds to a simultaneous drop in the values of L at the focal electrode sites. The observed slow cyclic variations in the temporal Lyapunov profiles imply attempts of the system to undergo a phase transition minutes before the seizure's onset. The analysis of the maximum rate of entropy production over space revealed an initial phase difference of minutes preictally at the sites overlying the seizure focus, which progressed to phase locking with a slow entrainment of the rest of the cortical sites shortly before the onset of a seizure. It is also conjectured that the abnormal spiking electrical activity of the brain plays a major role in the unfolding of the phenomeno...

this paper will report on an exciting and promising new methodology to quantify the EEG that is rooted in the theory of nonlinear dynamics. EEG characteristics such as alpha activity and seizures (limit cycles [1]), instances of bursting behavior during light sleep, amplitude dependent frequency behavior (the smaller the amplitude the higher the EEG frequency) and existence of frequency harmonics (e.g. under photic driving conditions) are extensively reported in the clinical literature. All these characteristics also belong to the long catalog of typical properties of nonlinear systems. By applying techniques from nonlinear dynamics, several researchers have provided evidence that the EEG is a nonlinear signal with deterministic and perhaps chaotic properties (for a review see [1-9]).