A major goal of dynamical systems theory is the search for simplified
descriptions of the dynamics of a large number of interacting states. For
overwhelmingly complex dynamical systems, the derivation of a reduced
description on the entire dynamics at once is computationally infeasible. Other
complex systems are so expansive that despite the continual onslaught of new
data only partial information is available. To address this challenge, we
define and optimise for a local quality function severability for measuring the
dynamical coherency of a set of states over time. The theoretical underpinnings
of severability lie in our local adaptation of the Simon-Ando-Fisher time-scale
separation theorem, which formalises the intuition of local wells in the Markov
landscape of a dynamical process, or the separation between a microscopic and a
macroscopic dynamics. Finally, we demonstrate the practical relevance of
severability by applying it to examples drawn from power networks, image
segmentation, social networks, metabolic networks, and word association.