Abstract : Experimental brain activity is known to show oscillations in specific frequency bands, which reflects neural information processing. For instance, strong oscillations at about 2Hz reflect tiredness and sleepiness, strong 40Hz oscillations indicate alertness. Changes of power in frequency bands indicate changes in information processing. For instance, it has been observed that strong activity about 10Hz and 2Hz emerge in electroencephalographic activity (EEG) when a subject loses consciousness in general anaesthesia. Numerical simulations of stochastic neural models have shown that such a change can be reproduced by changing the variance of external additive Gaussian uncorrelated noise. At a first glance, this is surprising since additive noise is not supposed to affect a system’s oscillatory activity or stability.
The presentation shows first how additive noise can affect the stability of a nonlinear system by applying stochastic center manifold analysis in non-delayed low-dimensional systems and delayed systems. Then, an extension to stochastic randomly connected network models shows that the observed effect also emerges. Applying random matrix theory together with mean-field theory demonstrates how additive noise tunes the stability and oscillatory activity in such systems. In sum, the mathematical studies provide an explanation why the brain’s oscillatory activity changes with changing experimental conditions.
