Nonlinear EEG analysis based on a neural mass model

The well-known neural mass model described by Lopes da Silva et al. (1976) and Zetterberg et al. (1978) is fitted to actual EEG data. This is achieved by reformulating the original set of integral equations as a continuous-discrete state space model. The local linearization approach is then used to discretize the state equation and to construct a nonlinear Kalman filter. On this basis, a maximum likelihood procedure is used for estimating the model parameters for several EEG recordings. The analysis of the noise-free differential equations of the estimated models suggests that there are two different types of alpha rhythms: those with a point attractor and others with a limit cycle attractor. These attractors are also found by means of a nonlinear time series analysis of the EEG recordings. We conclude that the Hopf bifurcation described by Zetterberg et al. (1978) is present in actual brain dynamics.