  We here study a network of synaptic relations mingling excitatory and
inhibitory neuron nodes that displays oscillations quite similar to
electroencephalogram (EEG) brain waves, and identify abrupt variations brought
about by swift synaptic mediations. We thus conclude that corresponding changes
in EEG series surely come from the slowdown of the activity in neuron
populations due to synaptic restrictions. The latter happens to generate an
imbalance between excitation and inhibition causing a quick explosive increase
of excitatory activity, which turns out to be a (first-order) transition among
dynamic mental phases. Besides, near this phase transition, our model system
exhibits waves with a strong component in the so-called \textit{delta-theta
domain} that coexist with fast oscillations. These findings provide a simple
explanation for the observed \textit{delta-gamma} and \textit{theta-gamma
modulation} in actual brains, and open a serious and versatile path to
understand deeply large amounts of apparently erratic, easily accessible brain
data.
