EEG spike and wave modelled by a stochastic limit cycle.

Abstract

Many reports based upon correlation dimension studies have suggested the chaotic nature of electroencephalographic spike and wave activity (SW). Another study found no evidence for this, showing that surrogate stochastic data generated from SW have the same dynamical properties as the original data. The present paper explicitly models SW as the output of a non-linear stochastic system. Non-linear non-parametric kernel autoregression is used to show that the attractor of this system may be a limit cycle. The addition of system noise originates a simulated time series with the same interspike interval variability originally hypothesized as chaotic. Tests performed on the correlation dimension obtained from the original data as well as from both linear and non-linear surrogates show that the noise-perturbed limit cycle model achieves the best fit to the original data. We conclude that SW is likely to be a form of stochastic disturbed limit cycle behaviour rather than chaos.