Some Theoretical Investigations in EEG Studies
  It is well known that Electroencephalography(EEG) and the respective evoked potentials have deep implications corresponding to specific cognitive tasks and in the diagnosis of several diseases such as epilepsy and schizophrenia. Some recent experimental results have already shown some evidence of chaotic activity in the brain. The Hodgekin-Huxley(HH) models, may yield geometrical solutions in terms of limit cycles and basins of attractors, but its implementation requires a priori knowledge of the kinetics of the innumerable conductances acting in a given set of cells. We are of the opinion that the EEG data should reflect the neuronal dynamics, and there should be some mechanism at the neuronal level which generates stochasticity compatible with the recorded data. In this paper we develop a theoretical framework to show that EEG dynamics may be governed by a suitably biased Vander-Pol oscillator which is closely related with the modified version of the FitzHugh-Nagumo(FN) model making extension of the ideas of dynamic causal modelling (DCM). Eventually we also give a prescription to compute the correlation matrices which may be tested empirically, for some small values of the parameters. 
I.Mitra