  The relation between spontaneous and stimulated brain activity is a
fundamental question in neuroscience, which has received wide attention in
experimental studies. Recently, it has been suggested that the evoked response
to external stimuli can be predicted from temporal correlations of spontaneous
activity. Previous theoretical results, confirmed by the comparison with MEG
data for human brains, were obtained for the Wilson-Cowan model in the
condition of balance of excitation and inhibition, signature of a healthy
brain. Here we extend previous studies to imbalanced conditions, by examining a
region of parameter space around the balanced fixed point. Analytical results
are compared to numerical simulations of Wilson-Cowan networks. We evidence
that in imbalance conditions the functional form of the time correlation and
response functions can show several behaviors, exhibiting also an oscillating
regime caused by the emergence of complex eigenvalues. The analytical
predictions are fully in agreement with numerical simulations, validating the
role of cross-correlations in the response function. Furthermore, we identify
the leading role of inhibitory neurons in controlling the overall activity of
the system, tuning the level of excitability and imbalance.
