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

Dynamic Brain Networks with Prescribed Functional Connectivity