Dynamic Brain Networks with Prescribed Functional Connectivity

In this paper, we consider stable stochastic linear systems modeling whole-brain resting-state dynamics. We parametrize the state matrix of the system (effective connectivity) in terms of its steady-state covariance matrix (functional connectivity) and a skew-symmetric matrix
$S$
. We examine how the matrix
$S$
influences some relevant dynamic properties of the system. Specifically, we show that a large
$S$
enhances the degree of stability and excitability of the system, and makes the latter more responsive to high-frequency inputs.